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TT 68-50 


NASA TT F 516 









O 00 

03 ^^^ Z( 

In i 



Published for National Aeronautics and Space Administration 
and the National Science Foundation, Washington, D. C. by the 
Indian National Scientific Documentation Centre, New Delhi. 






Izdatel'sWo "Metallurglya", 1966 


Published for National Aeronautics and Space Administration 
and the National Science Foundation, Washington, D. C. by the 
Indian National Scientific Documentation Centre, New Delhi. 


Contract NSF-C 

Translated and Published for National Aeronautics and Space 
Administration in accordance with the agreement with the National 
Science Foundation, Washington, D. C, by the Indian National 
Scientific Documentation Centre, Hill Side Road, Delhi- 12. India. 

© 1970 Indian National Scientific 
Documentation Centre, New Delhi. 

Printed and Published by INSDOC, Delhi- 12. 


The brochure gives a systematic accotmt of methodologi- 
cal problems of determining the thermal conductivity of refrac- 
tories. The material contained here would help improve experi- 
mental techniques, and generalize the factual data required for 
heat engineering calculations and for solving technological prob - 
leyns associated with refractory science and industry. 

The work is meant for engineering, technical end scienti- 
fic workers of refractory, glass and ceramic industries. 











The study of thermal conductivity of refractory materials 
continues to remain important even today. This is so, because, 
generally speaking, the investigations carried out so far applied 
only to particular cases and were marked by limitation of techni- 
ques and by the small number of systematic determinations. 

On the other hand, the present state of science and techno- 
logy in USSR and planned development of national economy have 
struck out special fields of work in the study of thermal conduc- 
tivity of refractory materials as a result of the introduction of 
new materials and the development of industries like thermal 
insulation, metallurgy, chemical industry, aviation, atomic 
industry and rocketry. Nov^adays, it is practically indispensable 
to deternnine the thermal conductivity: (a) of a large variety of 
refractory materials; (b) of very highly refractory materials 
such as oxides, zirconates, nitrides and carbides, in a w^ide 
range of temperatures (2 773-3273 K), right up to the melting 
point; (c) of refractory materials in vacuum (better than 10"TTim- 
HgCol) and under high pressures, in protective, regenerative, 
and oxidizing media, which correspond to the actual operating 
conditions of many refractories; (d) of refractory materials in 
the form of powders, readymade materials and special ceramics. 

The problems enumerated above form the basis of thermal 
physics, and involve the study of heat transfer during physico- 
chemical processes in structural materials at high tem- 
peratures [1]. 

Thermal conductivity is one of the most important physical 
characteristics of refractory materials. Till recently the data 
on the thermal conductivity of such materials was so meager 
that many theoretical aspects of Solid State Physics could not be 
verified. This can be ascribed to the insufficient study of the r- 

mal conductivity of refractory materials and to the imperfections 
in the experimental techniques. Moreover, the laws governing 
the variation of thermal conductivity as well as the methods of 
manufacturing refractory materials with given thermo-physical 
characteristics were not known> 

The investigations carried out. essentially related to parti- 
cular cases. In spite of the large number of published works on 
the subject [2], compact, accurate and vmiversally useful measur- 
ing apparatus were lacking. 

Modern science and technology of refractories has still to 
solve the problems of methodology pertaining to the determina- 
tion of thermal conductivity and the problems of systematic 
measurement of thermal conductivity, which are necessary for 
heat engineering calculations and for solving technological prob- 
lems of science and technology of refractories. 

At present, single -component, single-phase as well as 
compound, multiphase materials, and dense (even cast) but 
porous cerannics are being widely used. New materials are 
being developed. All of them require studies on their thermal 
conductivity characteristics. 

Thermal conductivity measurements of refractory insu- 
lators over a wide tenaperature range, right up to the melting 
point, yield valuable information for studying the various aspects 
of thermal conductivity in non-conducting crystals. This is only 
one of the actual problems of Solid State Physics. Such an 
experinnental study at temperatures above Debye temperature 
was not possible for quite a long time because of the non-availa- 
bility of sufficiently pure and dense samples of single crystals 
and polycrystals and the lack of requisite high tennperature 

In the present state of the science and technology of refrac- 
tories, the production of pure and dense materials would go a 
long way in formulating accurate methods for determining ther- 
mal conductivity. This, in turn, would enable the study of the 
variation of thermal conductivity w^ith temperature in the case of 
refractory insulators [3], 

While studying the thermal conductivity of refractories, 
it must be realized that a majority of these materials are 


heterogeneous, representing a ceramic or powdery mass con- 
taining a large number of pores and empty spaces. Therefore, 
for an understanding of heat transfer through these materials, 
it is necessary to determine the factors which influence the 
effective thermal conductivity over a wide range of temperature. 

The present work deals with the following: 

1. Study of those laws governing the variations in thermal 
conductivity of heat insulators, which affect most of the 
refractory materials. 

2. Investigation of parameters which influence the effective 
thermal conductivity of refractory ceramics. 

3. Description of the variety of equipment and experimental 
methods for determining the variation of thermal conducti- 
vity with temperature over a wide range of temperatures, 
applicable to most of the refractories, viz. heat insulators 
carbides, graphites, ceramics, and powders. 





1 . Choice of Method 

The apparatus available today are not sxifficiently developed 
for tackling all the complicacies met with in the determination of 
thermal conductivity of refractory materials. 

It is therefore -worth^while to develop a systenn of instru- 
mentation and techniques with which the thernnal conductivity of 
most of the modern refractory materials can be determined under 
conditions close to the actual working conditions. 

It is clear from a consideration of published works on the 
determination of thermal conductivity of refractory materials, 
that out of all the methods, those using a sphere, a cylinder or 
an ellipsoid under steady state conditions are by large the 
most accurate, convenient and noncontroversial. Their chief 
advantage is that the sample, which surrounds the heating source, 
is also made to "guard" the radial heat flow and so no special 
precautions are required except those that bring about this 
condition. But for adopting the methods using the sphere and the 
ellipsoid [4, 5], very careful preparation of samples is neces- 
sary and the samples have to be either ^jowders or of complicated 
shapes. Moreover, it is not possible to study a refractory 
ceramic or po^wder at temperatures near its melting point. 

From the point of view of sample preparation, the method 
using a hollow cylinder is more suitable. In this case,there may 
be errors due to heat exchange through the cylinder ends, but 
the shape of the samples is much simpler. 

This method is based on the measurement of the rate of 
heat flow under steady state by electrical means. Under this 


condition, the thermal conductivity is calculated from the 

where, T^ = the temperature of the hotter surface of the sample, 
at radius T2', 

Tj = the temperature of the colder surface of the sample, 
at radius ri ; 

q = 0. 24 I. V = rate of heat flow from the heating ele- 
ment when a current of I (amp) flQWS xinder a P. D. 
of V (volts) through the heating element, along a 
length X (of the sample). 

2 . Determination of Thermal Conductivity up to 1773 K 
(1500°C) in an Atmosphere of Air, Nitrogen, Carbon 
Dioxide, Argon or other Gases under Pressure and 
under a Vacuum of 1 x 10~'* mm Hg Col 

The diagram of the apparatus is shown in Fig. 1. It has a 
base 1 made of heavy steel disc with a vertical post 2 on which 
the other parts are mounted. The clamp 4, -which can move 
freely on the post and can be firmly fixed on it, has two semi- 
circular discs attached to it. The cylinder under test is mounted 
on one of the discs, while the other disc can be used for prepara- 
tory work and, if necessary, it could be used for a simultaneous 
second experiment with a separate electrical input. 

The test shell consists of a centrally mounted sample 13 
and two guard blocks 12, 15 on either side of it. The sample as 
well as the guard blocks are cylinders of 75 mm diameter and 
65 mm height with a central hole 19 to 21 mm dianneter. In the 
samples there are two holes for thermocouples (Fig. 2). Chan- 
nels, instead of holes^can be provided for the sake of simplicity, 
in materials having thermal conductivity less than 2 kcal/m. h. K 
(2,33 watt/m. K). 

The dimensions used for the cylinder (height 280 mm, dia- 
meter 65 to 75 mm, and a length-to-diameter ratio of 4.3 to 3. 7) 
insure a vuiidimensional cylindrical thermal flux in the central 
portion of the sannple. Such dimensions appear to be optimum, 
because the thickness of the cylinder is sufficient for setting up 


Fig. 1. View of an improved apparatus for determining thermal conductivity 
of refractory materials, which could also be used for refractory 

1 - base; 2 - post; 3 - nut fixing the post to the base, 4 - clamp with 
discs to mount the cylinder under test; 5 - cement asbestos holder 
for fixing the heating element; 6 -panel with electrical termitmls: 
7 - tubular former of the heating element; 8 - heating spiral; 9 - 
potentiometer wires and power leads; 10 - corundum tube; 11 - circu- 
lar end -insulators; 12 - lower guard; 13 - sample; 14 - thermo- 
couples placed inside the sample to measure the temperature drop; 
15 - upper guard; 16 - heat insulation; 17 - asbestos layer. 

appreciable temperature drop, even in the case of materials with 
relatively high thermal conductivity. Moreover, the lengths of 
the sample and the guards are such that standard bricks could be 
used without modifying these lengths. The cylindrical casing 16 
is made composite to facilitate assembly. It is to be noted that 
the sample and the guards need not be of the same material. The 
important requirement is that they should have nearly the same 
thermal conductivity aind about the same temperature coefficient 
of thermal conductivity. This aspect is especially important in 
the measurements on materials like fused quartz, fused magne- 
site, crushed quartzite, whose preparation and working in large 
quantities is technically difficult. Possible gaps between the 
ends of the cylinders are eliminated with the help of rings made 
of asbestos. Asbestos boards prevent heat loss through the ends 
to a certain extent, while the height of the sample is such that 
the flow of heat is only radial. 


Fig. 2. Samples for determining thermal conductivity of refractories up to 
1500OC (1773 K). 

a -Sample, with holes for thermocouples, suitable for measuring 
temperature in materials with thermal conductivity more than 
2 kcal/m.h.K. ; b - The same as above, ifith thermocouple channels, 
suitable for materials with thermal conductivity less than 2 kcal/m.hK 

At either end of the cylinder^ there is a covering of heat 
insulating material (e.g. , lightweight refractories) protecting the 
edges of the heater from which there is a considerable amount of 
heat dissipation. 

Qn the outer side, the cylinder is insulated with a 20 mm 
thick layer of highly porous, heat- insulating ceramic, consisting 
of lightweight Dinas and lightweight firebricks (chamotte) or 
better still, ultralight firebricks. 

The ultralight material possesses low thermal conducti- 
vity (0. 1 to 0. 2 kcal/m, h. K = 0. 16 to 0. 23 W/m. K. ). It is easy 
to machine and has satisfactory strength, A 1 mm coating of 
asbestos is given outside the ceramic insulation. This gives 
additional strength to the casing half rings and simplifies the 
filling of gaps between them. 

The casing half rings considerably increase the average 
temperature at which the measurements are made. They de- 
crease the relevant temperature drops (between hot and cold 
faces) in the measurements of thermal conductivity and conse- 
quently result in better accuracy of the measurements. The 
application of the insulating layer decreases considerably the 

povi^er consumption even at very high temperatures and reduces 
distortion of isothermals on the cold surface of the cylinder due 
to convection. Nevertheless, the decrease in the temperature 
drop reduces the accuracy of temperature drop measurement 
and increases the time required for realizing the steady state 
condition. The dimensions of the casing are so cHosen as to 
yield the best results. 

The other details of the apparatus depend on individual 
requirements. Two variants of the apparatus have been develop- 

1. For measuring the conductivity of highly jorous (light- 

weight) refractories up to 1473 K (1200°C). For this purpose, 
the apparatus has a through-heating element fixed in two holders 
which also act as electrical terminals (Fig. 3). 

Fig. 3. View of the apparatus using through -heating elements with ternntials 
at each end. 

1 - base; 2 -post; 3 - electrode holders; 4 - copper electrode; 
5 - supporting clamp; 6 - 'ower guard; 7 - sample; R - upper guard: 
9 - corundum former of the heater; 10 - heating shiral; 11 - thermo- 
couples; 12 - hole for the thermocouple leads; 13 - nnlcr casing; 
14 - rings of lightweight ceramic; 15 - copper terminals of the heater. 

Terminals 15 are of red copper and are insulated by ebo- 
nite bushes from the metallic holders soldered to the slide. 

The cylinder under test (the sample and the guards) is 
shown in Fig. 2. The internal hole has a diameter of 13. 15 to 
14. 00 mm. In addition to the central hole there are channels 
for thermocouples on the inner and outer surfaces of the cylin- 
der, and channels for thermocouple leads on the end faces. For 
accurate measurements, a drilled hole to suit the thermocouple 
is used, instead of the channel (Fig. 2). 

Because of simple shape and small dimensions of the 
sample, it is possible to study not only commercial products, 
but also experimental samples die -cast in the shape of a 
cylinder ■with a central hole. The thermocouple holes and 
channels are made on samples in the "wet" (unbaked) condition. 

2. For measu'-ing thermal conductivity of refractories up to 

1773 - 1873 K (1500-1 600°C). The apparatus (Fig. 1) has already 
been described in the previous section. In this case, the central 
hole is increased to 19 to 21 mm diameter. On the one hand, 
this facilitates bringing out through one end all the lead wires 
of the heaters, as well as those for temperature measurement 
with a minimum of heat loss. On the other hand, it enables the 
use of the refractory platinum -rhodium wire (for heater), which 
is not possible in the previous apparatus because of very low 
resistance of platinum- rhodium. 

The heater is uniformly wound on a former which remains 
sufficiently rigid even at the highest temperatures in use. The 
former is made of corundum, either by extrusion or when the 
diameter is large (25-3 mm), by casting in gypsum molds. The 
required holes are made either in the "green" or in the "initially 
burnt" tube. Then the body is finally baked till it acquires the 
minimum porosity. 

It is important to insure uniformity in winding the heater 
wire on the former. This is achieved as follows: tw^o w^ires, 
namely, the heating wire, 0.5 to 0.6 mm diameter, (either 
nichrome, platinum- rhodium, or special alloys) and a secondary 
wire (nichrome), 0. 3 mm diameter, are close wound, touching 
one another, on the fornner. After winding the whole length of 
the former and fixing the heating spiral, the thinner (nichrome) 
wire is \xnwo\ind, leaving a uniformly wound heating spiral. The 

heater wire is then cemented on to the former with corrax 
(molten corundvim) or with a mixture of •well pow^dered alumina 
and 10% (by weight) clay or kaolin, in order to get better baking 
qualities. Such a coating bakes well on to the former and is 
fotind suitable for all types of heating elements including those 
for very high temperatures of 1773-1873 K (1500-1600°C) at the 
sample, i. e. when the heater temperature is as high as 1873 to 
1923 K (1600 to 1650°C). 

The cement coating for heating elements of the type with 
two end terminals (Fig. 4b), which w^ork up to temperatures of 
1373 to 1473 K (1100 to 1200°C), can be a mixture of well 
powdered magnesite burnt to 1873 K (1600°C) and a small 
quantity of water glass. Although magnesite powder smoothens 
out temperature variations along the heater length and in between 
the windings due to its greater thermal conductivity, yet it 
decomposes at temperatures above 12 73 K (1000°C) and reacts 
with the sample and the heater former. 


Fig. 4. Heating eleinents. 

a -with single -end feed. 

1 - potentiometer leads; 2 - the points to be welded on to the heating 
spiral; 3 - hole drilled in the former; 4 -former; 5 - corundum tube . 

b - tvilh two end contacts. 

1 - heater contacts; 2 - potentiometric leads; 3 - points for welding 
on to the healing spiral; 4 - hole drilled in the former; 5 - corundum 
tube; 6 -porcelain insulation; 7 ■ connection of heating spiral with 
the contact. 

The equipment described above was meant for measuring 
the heat flow in absolute terms, i.e. the results are not related 
to reference scales or models. It is therefore important to 
measure accurately the quantity of heat entering into the sample. 
In the present case, the quantity of heat flow was measured 
electrically. The electrical power dissipated in the heater covild 
be a measure of the thermal flux. The current iwas measured 
outside the heater. The accuracy of measurement is solely 
determined by the degree of precision of the measuring instru- 
ment. Therefore, the accuracy of pow^er measurement depends 
on the accuracy of measuring the voltage drop across the length 
of the sample. 

To measure the voltage drop corresponding to the quantity 
of direct heat flow into the sample, the heater element was made 
with two holes drilled symmetrically at a distance of 65 to 70 mm, 
in the central portion of the body. In the half-baked stage, the 
holes were made >vith an ordinary drill but when they were 
required to be done on a finished former, they were made with 
an ultrasonic drilling machine. Through these holes in the 
former, the heater was connected to potentiometer leads which 
were also made of the same material (as the heater). In order 
to get reliable electrical contact, the wires were arc-welded and 
the weld was covered up in a corundum case. 

The potentiometric measurements enabled calculation of 
the thermal flux to be made in two ways: (1) by computing the 
power consumed in the wrhole heater and more accurately, (2) by 
computing the power consumed in the central portion of the heat- 
er. It was then possible to compute the actual specific power. 

General view^ of the two -end heating element inade with 
nichrome or special alloys (alloy 2, EI 626) is shown in Fig. 4b 
and its single-end version with platinum wires is shown in 
Fig. 4a. The single-end version enables minimizing the losses 
through the ends of the cylinder. To avoid short-circuits, two 
of the three wires are encased in corundum sleeves. 

Wire type heaters having potentiometric leads are more 
difficult to fabricate than the ordinary ones. The heating and the 
secondary wires are wound in parts: they are first wound up to 
the first hole, the measuring w^ire is welded on and then w^inding 
is done up to the second hole, where the next measuring wire is 


The heaters have the following parameters: 

1, The heater with two-end contacts, for tennperatures up to 
1473 K (12 00°C) at the hot face of the sample (Fig. 4b). 

The tubular former of coriindum has a length of 300 to 
320 mna, outside diameter of 10 mm, inside diameter of 4 to 
6 mm, length of the central portion between the holes for the 
potentiometer leads 70 to 75 mm, heating length of 2 70 to 
280 mm. About 7. 5 m nichrome wire of 0. 6 nnnn diameter, 
resistance 30 to 35 ohms, has been used. The resistance of the 
alloy of diameter 0. 5 mm is about 70 ohms, ■whereas that of the 
material EI 626 of diameter 0.5 mm is about 50 ohms. The 
resistance did not increase appreciably with increase in 
temperature . 

2. Platinum- rhodium heater (10% Rh) with single-sided feed, 
for temperatures up to 1773 K (1500-1600 °C) at the hot face 
(Fig. 4a). 

The tubular fornner of corundum has a length of 3 00 to 
32 mm, outside diameter 15 to 16 mm, internal dianneter 10 to 
11 mm. The central portion is 70 to 75 mm long. The zero 
current resistance of the central portion of heater at room tem- 
perature is 4. 8 ohmsj and that of the whole heater 13. 8 ohms. 
Resistance increases rapidly with increase in temperature and 
becomes 40 to 50 ohms at 1773 K (1500 °C). 14 m of platinum- 
rhodium wire of 0. 5 mm diameter is wound on the heater. 

Platinum- rhodium wires with 20 and 40% Rh having a 
higher melting point (up to 2123 K,i. e., 1850 °C) were also used. 
But the refractoriness of this wire could not be fully utilized, 
since the body deformed at temperatures higher than 1873 K 
(1600°C); moreover, the wire with a higher content of Rh is 
extremely brittle, which complicates the winding operations 
and results in pulling up the potentiometer leads, etc. Uni- 
formity of winding and the length I of the central portion were 
determined by X-ray photography. 

The circuit for temperature measurement along w^ith the 
wiring and instruinentation for power measurement complete 
the setup for determining the thermal conductivity. The power 
supply consists of a 1 k'w stabilizer transformer supplying 220 V 
to LATR-1 (power regulator), which feeds the heater. A volt- 

meter and an ammeter measure the voltage emd current in the 
heater. The voltage drop in the central portion of the heater is 
recorded by a separate voltmeter. The temperature-measuring 
circuit consists of thermocouples, their switches ajid a potentio- 
meter for measuring the thermo-e. m, f. 

The cylindrical shell consists of the asbestos sheet, heat 
insulation rings, the upper and lower guards, the sample and its 
insulation rings. The alignment of the central holes must be 
insured while assembling the shell. The heater is placed inside 
the shell. 

The heater is so adjusted -with the help of the electrodes 
that its central portion sits in juxtaposition with the sample. 
The electrode carriers are fixed to the post and the heater is so 
clamped to the electrodes that the insulating sleeves and the 
potentiometer leads rest inside special grooves cut in the elec- 
trodes. The springs of the electrodes take up the thermal expan- 
sion of the body. After fixing the heater to the electrodes, the 
cylindrical section is insulated with the two semicircular rings 
and all gaps and clearances are filled with asbestos. 

The preparation for the apparatus with single-sided con- 
tacts is simpler. The heater (Fig. 4, a) is firmly fixed in the 
cement asbestos holder. The assembling is done by lowering 
the guards, the sample and the cylindrical end insulation on the 
heater. Thereafter, the composite and shaped case made of 
heat insulating ceramic is put on. This arrangement reduces 
the heat losses considerably. 

The necessary voltage is approximately set with the vol- 
tage regulator. When the temperature of the hotter surface 
reaches the necessary level and the sample starts getting hot, 
the voltage is reduced manually till steady state heat flow is 
established, i. e. the temperatures of the hot and the cold faces 
do not change any more with a constant power input. Three 
observations are taken at intervals of 10 minutes each. 4 to 5 
values of the thermal conductivity at different temperatures can 
be determined by this apparatus in 8 to 9 h. 

Measurements with Pores of the Material Filled with 
Different Gas es at Atmospheric and Smaller Pressures. 

Due to the compact and self-contained nature of the equip- 
ment, it could be used w^ithout any alteration, for measurements 


in vacuum (right up to 1x10"'* mm HgCol) as well as under any 
gaseous atmosphere. For this purpose, the entire assembled 
apparatus was placed in a standard vacuum chamber of large 
volume (0, 5 m^). The power leads and the temperature -measur- 
ing leads were run along the leads of the vacuum chamber. The 
air was pumped out of the chamber with rotary and oil diffusion 
pumps. The rate of air exhaustion was 1000 liters per second. 

For taking measurements under a given gaseous atmos- 
phere, the vacuum chamber was emptied to 1x10""* mm HgCol 
and then filled with the required gas. In spite of the fact that 
the ceramic released some gas, the large volume of the cham- 
ber insured that the necessary atmosphere and the required 
pressure were sustained for sufficiently long periods. During 
measurements in vacuum, the heat insulation of the apparatus 
casing is more effective, since the conductivity of the ceramic 
is considerably reduced. 

Measuring the Effective Thermal Cond uctivity of Powdered 

The abovementioned equipment and method were used for 
this purpose. How^ever, a hollow cylinder (Fig. 5), filled with 
the powder under test, was used instead of the cylinder and the 
casing described previously. The cylinder was made from heat- 
insulating durable bricks (outer wall) and a corvindum tube 
(inner w^all), and asbestos was used as additional external insu- 
lation as well as cementing medium. A cover, placed from 
above, fixed the corundum tube securely. The cylinder was 
filled w^ith the powder through four openings in the cover. 
Dimensions of the cylinder were: height 203 mm; outside dia- 
meter 91 mm; internal diameter 20.5 mm. Platinum vs plati- 
num-rhodium thermocouples, for measuring the temperature 
differential, were installed on the inner surface of the cylinder, 
viz. , on the corundum tube and at the ceraraic wall. The hot 
junctions of the thermocouples were situated at the middle of 
the cylinder height. 

The distance between the thermocouple hot junctions was 
constant and was determined by X-ray photography or by direct 
measurement. The packing density Tvas calculated from the 
mass of the powder and the volume of the cylinder. In other 
respects the method was identical with that for baked refrac- 


Fif^. 5. View of the hollow cylinder, filled with the powder under test. 

1 - cover; 2 - corundum sleeve for the thermocouples; 3 - cylinder 
wall made of lightweight firebrick: 4 - hot junction of the thermo- 
couple; 5 - asbestos insulators; 6 - corundum tube (internal surface of 
the cylinder); 7 - windotvs in the cover through which the powder is 
filled into the cylinder; 8 - thermocouple leads. 

The maiximuiii temperature of the measurements ■wa.s 
1473 K (1200°C). At higher temperatures (1300 to 1400°C on 
the hot face), the smaller particles (less than 0.2 mm) started 
beiking appreciably. Measurements under such conditions were 
meaningless, because the material behaved as a ceramic rather 
than as a powder, and the ceramics have heat transfer proper- 
ties entirely different from those of powders, particularly at 
lower temperatures (373 to 873 K, i.e. 100 to 600°C). 

Errors in the Method 

Let us estimate the relative error of the methods des- 
cribed above. In the case of the hollow cylinder, the coefficient 
of thermal conductivity was determined from equation (1), from 
which the general expression for the maximum theoretical per- 
centage error is equal to: 


i!i> TaI^AV fikTi + ATsL 1 /A^i A^i.'V till H 

Let us now consider the error contributed separately by 
each of the terms into the total error. 

The precision of the instruments used (voltmeter and 
ammeter) determines the errors in measuring the voltage and 
current. In our case the accuracy was 0.5% of full scale deflec- 
tion. Since the measurements, in our case, were made close to 
the full scale deflection it can be considered that: 

This error is small and the total error introduced by it in 
heat flow^ measurements is 1%. However, this error could be 
reduced by using instruments of higher precision, say 0.2 or 
even 0. 1%. The accuracy of heat flow measurements, due to 
this, can then be improved to a theoretical value of 0.2-0.4%, 
which is a small qujintity. 

The error in determining the radii of points, where thermo- 
couple hot junctions are placed, is at least 0. 5 mm, i. e. , 
J^f. = ^^ =0.5 mm. (The minimum error is determined by 
the thickness of the thermocouple w^ire. For a wire thickness of 
0. 5 mm and jimction thickness of 1 mm, this error cannot be 
less than 0.5 mm). Lengths were measured by X-ray photo- 
graphy so as to limit ^Y" to 0.5 mm. 

The length of the central portion of the heater and the posi- 
tions of the thermocouple hot junctions inside the sample, w^hen 
ready for measuring, were also determined by X-ray photo- 
graphy, which w^as done on commercially available equipment. 

While photographing along the ends of the cylinder, special 
and sufficiently precise orientation of the end planes perpendi- 
cular to the ray axis was necessary. Moreover, in this case, 
due to the divergence of the rays, a half- shadow w^as obtained. 
These shortcomings could be avoided by photographing parallel 
to the ends. The small contrast at the edges of the hole, due to 
negligible difference in the thickness of the absorbing layers, 
could be improved by inserting steel fixtures into the holes 
while photographing. 


The increase in dimensions, obtained due to ray diver- 
gence, ■was determined by nneans of a reference strip. It is 
important to consider the increase in dimension for length ^ 
only; the ratio of the radii is not affected by the increase. 

As a result of all this, the accuracy in estimating the dis- 
tance, /^t =0.5 nim was attained. 

For our sample: r2 = 7.2 to 9.5 mm (average 8.4 mm); 
T-, = 35. 6 to 38. 8 mnn (we can take an average of 37. 2 mm); 

In— ^ = 1.41 to 1.68 (average 1.55); A'^ =0.5 mm; £ = 65 

to 75 mnn. Substituting these values, the total error due to all 
the linear measurements seems to be 6.5%. This relatively 
large amovint of error could probably be reduced by using thinner 
thermocouples (0.2 to 0.3 mm). 

The error in temperature measurements depends on many 
factors --the accuracy of instrunnents, conformity of the thermo- 
couples to standards, temperatures used for measurement, and 
conductivity of the material being tested, etc. 

Thermo-e. m. f. of the thermocouples was measured with a 
potentiomieter of type PPTV-1 or of type PPTN-1, using a mir- 
ror galvanometer of type GZS-47 and standard cells of class 2. 
This instrumentation had a sensitivity of 0. 01 mV, which means 

A"^ - ^7"=i°, for platinum vs platinum- rhodium thermo- 
AT^s^OkTj^ =0. 2°, for chromel-alumel thermocouples; 
A7: = AT =.0.1°, for chromel-coppel thermocouples. 

The temperature differentials depend mainly on the con- 
ductivity of the material as well as on the temperature, at which 
they are determined. Typical values of these differentials and 
the value of the percentage error introduced by them in these 
experiments on refractories, having the usual values of conducti- 
vity, are shown in Tables 1 and 2, respectively. 

Obviously, for a given temperature range and for a given 
conductivity of the sannple, suitable thermocouples can be select- 
ed so that even at the lowest temperatures of measurement the 



Variation of thermal conductivity of material, with temperature differential {T2 - T,), at different 

average temperatures of measurement 

Temperature differentials (T^ - Ti) at temperature of measurement, °C, (K) 


o r- 

<^ <^ 00 fn (T, 

ot^or~ or~- or- or-or~ 00 Oi-ho 




(M'^roin Tt<vO uir- vooc t— o cor-i a>i-i o^ •-< ^ Mr-4 <*^ 

Magnesite 6. 5 

Forsterite 17 

1;^ Dinas (Light- 
weight) 45 
Firebrick or 
(lightweight) 45 

17 34 53 75 97 124 148 181 213 258 

36 64 92 125 161 195 230 26? 308 351 392 

73 118 164 213 262 304 355 400 

91 138 190 242 293 339 392 432 471 514 552 599 


Percentage errors in measuring temperature drops, with different types of thermocouples, as a function of the 

test temperature 


WT* 1 on 
Percentage error -^ — '—— — at temperature of measurement, °C, (K)* 

Tz -Ti 

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 
(373) (473) (573) (673) (773) (873) (973) (1073) (1173) (1273) (1373) (1473) (1573) 

^ Magnesite 15.4 

°^ ForaterLte 5.9 

Dinas (lightweight) 2.2 

Firebrick (light- 
weight) 2.2 

For platinum vs platinum- rlkodium thermocouples 





























1.1 0.7 0.5 0.4 0.3 0.3 0.3 0.2 

For chromel vs alumel thermocouples 


0.2 0.2 0.2 


3. 1 



















Dinas (lightweight) 










Firebrick (light- 












♦For chromel vs.coppel thermocouples, the percentage error is half that for chromel vs alumel. 

accuracy in measuring the differential may not be less than 3%. 
With increase in temperature, this error decreases rapidly. 

Therefore we have, for errors in temperature measure- 
ment, the following: 

Temperature, K (°C) 

373 (100) 3. 1 

573 (300) 0.6 

773 (500) 0.3 

973 (700) 0.2 

1173 (900) 0.1 

Summing up all the errors, we have: 

Temperature, K ("C) 

373 (100) 10. 6 

573 (300) 8. 1 

773 (500) 7.8 

973 (700) 7. 7 

1173 (900) 7.6 

In this method, the major portion of the error is due to 
errors in linear measurements; the other errors are compara- 
tively small. 

Errors in linear measurements are also significant in the 
ellipsoid and hollow cylinder methods because the distance bet- 
ween the thermocouple junctions is only 10 mm. However, some 
authors [26, 4, 5], do not include the error due to linear mea- 
surements in the total errors while stating their errors. 

In the abovementioned method, there is another funda- 
mental difference compared to the American shell methods, 
viz. that the thermocouple wires traverse an isothermal zone 
and this reduces the heat conduction through them. Repeata- 
bility of the results was verified in the case of Dinas. The mean 
square deviation for the whole of the temperature range is 8%. 


Verification of the Heat Losses Along the Heat Flow 

This heat dissipation in the hollow cylinder method is 
considerably less as compared to that in the flat plate method, 
due to the shape of the sanaple and the heater. (In the case of 
the hollow^ sphere and the hollow ellipsoid, the heat losses are 
completely eliminated). Keeping the length»to-diameter ratio of 
4:1 to 3:1 for the cylinder, the heat losses were studied in the 
case of the tw^o-end heater type apparatus. 

One of the nnethods for this consists in placing thermo- 
couples on the upper and lower guard blocks, in positions corres- 
ponding to the thermocouples on the hot and cold faces of the 
sample. Experiments were conducted on lightweight Dinas, 
whose thermal insulation properties are such that they can only 
enhance the sideway heat losses. In other words, the experi- 
mental conditions were more rigid than met with in practice. 
Results of experiments are shown in Table 3. 

Distribution of temperatures on the cylinder under test, °C 

Hot face 

Cold face 








mm) Ruard 





(r = 7. 7 mm) 

(r=7. 8 mm) 

(r=35. 4 mm) 









22 7 











































It is seen that at the first thermocouple near the hot face, 
there is practically no variation of temperature along the whole 
length of the cylinder (i. e. , over a length 2 *. ) provided the 
nontxniformity of cylinder radius r is taken into account. 


The temperature of the cold face ho'wever, varies to a 
certain extent (along the length), mainly because of the heat 
losses. At a hot face temperature of 1073 K (800°C), the 
temperature drop over the length £ is 47°C, while the radial 
temperature drop is 400OC. And, considering the nonuniformity 
of the sectional areas, the heat losses amount to only 2%. 

/ "X ( T '— T '^ 

Q _ Z^ JL -1 1: - iTvi, for the main radial heat flow 



K.— J ) for losses through the ends (4) 

In our case Ti - T' f=^ 400° ; 1 = 65 mm; T, - T, ?=J47°; 
1, (752 . io2), 2 1 


therefore, ^ 


The heat flow losses account for 2%. This is close to the 
value computed on the basis of power consumption in various 
sections of the heater; in fact, it is less than that. This is so, 
because w^e have considered only a part of the cylinder. 

Experiments with samples of different heights give a defi- 
nite confirmation of the negligible heat losses through ends, 
during precise determinations of thermal conductivity. 

Results of measurements on samples of 65 mm height 
(corresponding to the height of comnnercial refractory) and 
35 mm height are shovm in Fig. 6. The reduction in height of 
the sample in the second case was compensated by increasing 
the height of the guards. 

The experimental results show that the values of the ther- 
mal conductivity, determined on samples of different heights, 
are the same within the limits of errors of measurement. In 
addition, verification was done on three types of refractory 
ceramics differing greatly from one another in conductivity and 
temperature characteristics. Moreover, the results of experi- 
ments on models of different heights indicate the possibility of 










200 WO BOB 8oe woo mo two 
Temperature, Oq 

Fig. 6. Verification of the possibility of reducing sample height. 

a - "Satkin" magnesite^i.e. magnesite from Satkin; b - Dinas; 
c - light for sterite. 

1 - samples of 65 mm height; 2 - samples of 35 mm height 

conducting tests on small size samples oi materials which are in 
short supply or difficult to man\ifacture. 

Qualitative checks, made try several methods, on the heat 
losses in the apparatus with a two-end heater show, that heat 
dissipation due to radial flow accounts for not more than 8% and 
under better insulation conditions it is practically nil. More- 
over, such end losses do not affect the conductivity measure- 

In the improved apparatus (Fig. 1) the losses through the 
ends are so small that they can be neglected. 

While developing the apparatus, it was important to com- 
pare the results obtained by the method w^ith other known 
methods on known materials, which are usually taken as 
reference materials. The choice of a refractory insulator, as 
a reference material is difficult due to technical difficulties in 
getting very pure non-ceramic samples. A comparatively good 
material is quartz glass, which is free from at least one defect, 
namely, the presence of pores. 


The results of previously published works [27 to 29j were 
grouped together [2 7] to draw an averaged curve (Fig. 7, curve 1) 
for fused transparent quartz, in which the accuracy of measure- 
ment was + 10 to 12%. 

Thermal conductivity measurements of quartz glass in the 
present apparatus gave a temperature -thermal conductivity 
curve (Fig. 7, curve 2), which is somewhat lower than the 
published values [27] mentioned above, but the accuracy of » 
measurement was +8%. In the middle of the temperature range 
(700 to 1000 K), the difference between the two curves lies 
within the limits of accuracy of the curves. At the beginning 
and at the end of the curves, the disagreement is more than the 
total experimental error. It must be noted that quartz used for 
experiments was cut out from big blocks which had a fairly large 
amount of impurity. This could have caused the disagreement 
in the results, especially at more than 1000 K. 

■^ 3.0 


- 3.'i3 


- 7.33 S 

- t.WJ 


313 573 773 973 1173 1373 1573 
(WO) (300) (5001 1 700) (900) a 100) (1300) 

Temperature K (°C) 
Fig. 7. Comparison of data on thermal conductivity of quartz glass. 

1 - averaged curve as per published data [27-29]; 2 - the curve from 
the author's data. 

It should be noted, however, that even with the errors 
mentioned above and the differences in purity of the samples, 
the tests show that the apparatus and the experimental method 
are sufficiently reliable. 

Thermocouple Positions In side the Sampl e 

The thermocouples on the sample are situated near the 
outer ajid the inner surfaces of the cylinder. They can be 
placed either in channels cut along the cylinder surfaces and 
covered with a mixture of powdered alumina or they can be put 
in holes, 1.5 to 2 mm diameter, drilled at a distance of 1 to 
3 mm from the surfaces. 


The junctions are kept at the center line of the sample. 
For measureinents in materials with thermal conductivity of 1 
to 2 kcal/m. h. K (1. 16 to 2. 33 watt/m. °C), any other convenient 
way of fixing the thernnocouples in channels can be resorted to. 
For more conducting samples and for precise measurements, 
the thermocouples should be placed inside holes, because the 
temperature distribution around couples, especially at the hotter 
junction, gets disturbed by filling with alumina or even by the 
sainple material itself. The distortion in temperature distri- 
bution is most noticeable >vhile working in vacuum, where the 
loosely baked filler material acts as an additional thermal 

The thermocouple hole is filled with a fine powder of the 
sample material. An increase in the hole size beyond 1.5 to 
2 mm leads to uncertainty of the position of the junction and it 
is possible that it may not touch the wall of the hole. 


Main characteristics of the apparatus described above 

a. possibility of measuring in practically jmy atmosphere 
(air, vacuum, or special atmospheres); 

b. possibility of testing specimens of commercial products 
(without placing limitations on grain, porosity and other 
technological factors) and also laboratory samples; 

c. relatively snnall size of sample facilitates experiments on 
short-supply jind expensive samples. Besides this, the 
geometry of the sample is simple; 

d. small dimensions of the apparatus and consequently 
smaller time constant; 

e. a wide range of temperatures: 3 73 to 1773 K (100 to 

f. possibility of measuring thermal conductivity from very 
low values (0. 2 kcal/m. h. K, i. e., 0. 23 watt/m. °C) to 
relatively high values (10 to 20 kcal/m. h. K, i.e., 11. 63 
to 23.3 watt/m. °C); 

g. satisfactory accuracy of measurements, good reproduct- 
ibility and low thermal losses. The choice of one of the 


steady state heat flo'w methods makes the apparatus as a 
whole simple and the computation of thermal conductivity 
also becomes simple; 

h. low time constant of the apparatus enables 4 to 5 conducti- 

vity measurements at various temperatures in 8 to 9 h. 
The number of observations reduce to 3 to 4 for heat 
insulators, particularly in the case of determination of 
the effective value of thermal conductivity of powders, due 
to the slow heating up. 

Because of the simple construction and easy availability 
of the requisite instruments, and because of the simple nneasur- 
ing procedure, the apparatus has been widely used in many 
scientific and technical research works. It has been more 
particularly used for the control of thermal conductivity value 
in the manufacture of light refractories and for studying the 
thermal conductivity of hard compounds of refractory oxides. 

3. Special Methods for Determining Thermal Conducti- 

The abovementioned apparatus and the measurement 
technique for determining thermal conductivity could be utilized 
for various special investigations, such as measurements in 
vacuum up to 1973 K (1700 °C) and simplified measurements up to 
1773 K (1500°C), as well as for studying thermal insulating pro- 
perties of refractory ceramics. The necessary modifications of 
the apparatus for these cases are briefly discussed below. 

The C omp arator Method Jfor D etermining Thermal 

The cylindrical shell (outside diameter up to 100 mm, 
internal diameter 14 mm), consisting of the sample 6, symme- 
trical guards 4 and heat insulating rings 3, is fixed on the metal 
base 10 of the apparatus (Fig. 8). The guards, having a thermal 
conductivity close to that of the sample and the lightweight insu- 
lation rings, are meant for reducing the heat losses along the 
axis of the apparatus. A standard carborundum heater 3Z0 mm 
long and 12 mm diameter 5 is fixed inside the cylinder on center- 
ing spring clamps. The clamps are insulated from the body and 
are cooled with flowing water. The sample is cylindrical, 65 
to 70 mm high and up to 100 mm diameter. A through-hole 


14 mm diameter is drilled in the center of the sample to hold 
the heater and there are three holes for the thermocouples 11. 

Fig. 8. View of the apparatus for measurement of absolute thermal conducti- 
vity by comparison method. 

1 - electrode holder; 2 -air cooled electrode; 3 - rings of lightweight 
insulation; 4 - guard; 5 - heater; 6 - sample; 7 - powdered alumina 
layer; 8 -fixing column; 9 - cement asbestos; 10 - base; 11 - thermo- 
couples; 12 -probe. 

Temperature is measured with platinum vs platinum- 
rhodium thermocouples. For colder surfaces, chromel-alumel 
thermocouples may be uped. 

While determining tllermal conductivity with this apparatus, 
the annular layer along the whole length of the sample between the 
third and second thermocouples (T3, T^^ is taken as the material 
under test. The layer between the second and first (T2, Tj) 
thermocouples is taken as the reference material of known 
thermal conductivity. 

Then, the thermal conductivity ( ^t-^-t.^. ) of the material, 
at the high temperature layer (T3 — T2), is expressed in terms 
of the conductivity ( >.-j- -Xj. ) o^ the reference layer (T2-Tj), as 
follows : _ _ 



where T3, T2, Ti are the temperatures at radii r^, rz, rj, 
respectively. (The temperatures are measured with thermo- 
couples and distances between them are measured either by 
X-ray photography or by direct measurement). 

The low temperature (up to 1273 K) thermal conductivity 
value of the sample, used for calculating the required thermal 
conductivity while testing with carborundum heater (up to 
1773 K), is determined on the sanne sample and with the same 
test cylinder as in the absolute method*, using the nichrome 
heater described before. 

An attempt was also made to measure absolute thermal 
conductivity by means of the heat input of the sample heated 
with carborundum heater. For this purpose, the voltage drop 
was measured under steady state conditions, in the central por- 
tion of the heater, by a momemtary contact of steel pins 
(probes) connected to a voltmeter. The measured variation of 
thermal conductivity of a zirconium dioxide sample is shown Ln 
Fig. 9. 















• -Z 


J7J 575 113 313 1173 1313 1573 IW' 
[WO) (300) 1500) (700) (300) (1100) (1300) (1500) 

Temperature K (°C) 

VS3 W 

a93* g 

0.1 ^ 

Fig. 9. Absolute thermal conductivity vs temperature relationship for zirco- 
nium dioxide, determined by the comparator method. 

1 - by absolute measurement and 2 - by comparison method. 

While making the measurements on forsterite, the scatter- 
ing of experimental points did not exceed 7% at the hot face tem- 
perature of 873 K (600 °C), 3% at 1573 K (1300 °C) and 1% at 
1673 K (1400 °C). 

Comparison of the data obtained for thermal conductivity 
of magne site -chromium sample by this apparatus, w^ith the data 
of A. F. Kolechkova and V. V. Goncharov [39] on the sanne 

*'fhe terms 'Absolute method" and "absolute thermal conductivity" are used 
to indicate that the measurement does not require a reference material. 


material, shows that the maxiinuin divergence in the results at 
high temperatures falls within the limits of accuracy of the 

The method is slightly cumbersome, but it enables to obtain 
the temperature-conductivity relationship up to high tem- 
peratures, i. e. up to 1773 K (1500 C) by using the widely used 
carborundum heating elements and nichrome wire, thereby avoid- 
ing the platinum- rhodium wire which is in short supply. 

Determining Thermal Conductivity up to 1973 K (1700°C), 
in Vacuum 

Measurement of conductivity above 1773 K (1500°C) was not 
possible in the apparatus described in Section 2, because of the 
unavailability of high temperature heater wires which could 
satisfactorily work in vacuum. Since tungsten and molybdenum 
could be used as heating wires in vacuvun, a modification of the 
apparatus to measure up to 1973 K (1700°C) was possible. 

The following changes were made to suit the measurements 
in vacuum: 1. The asbestos -covered lightweight refractory insu- 
lation layer was replaced by a more insulating layer of light 
refractory material having high alumina content (the asbestos 
was replaced because of copious gas occlusion at high tem- 
peratures); 2. Water-cooling vras dispensed with, heavier copper 
electrodes were used and the copper contacts for the heater were 
replaced by graphite; 3. Tungsten and molybdenum were used as 
heating wires. The parameters of typical heating elements are 
given in Table 4. 

During the measurements, the apparatus jWith the heater 
fixed inside it, was placed in a 0. 5 m^ vacuum chamber and the 
power supply lines and measuring wires were led through the 
vacuum inlet. To conduct measurements up to the highest tem- 
peratures, the more powerful autotransformer type RNO-250-10 
was used instead of type RNO-250-2. 

It was not possible to weld the potentiometer leads to the 
tungsten and molybdenum wires and to keep the junction inside 
a sleeve, because of frequent breakage of the jimction. The 
voltage drop was therefore measured at the ends of the heater. 



Special high temperature heaters for measuring thermal con- 
ductivity in vacuum 



Former (corundum tube): 

length, mm 

outside diameter, mm 

Molybdenum wire: 

length of heating section, mm 
wire size, mm 

No. of turns 

Approximate wire length; m 

Electrical resistance, ohms: 

w^hen cold 

at 773 K (500°C) on hot face 

at 1873 K (1600OC) 

at 1973 K (1700°C) 
















* A temperature of 1903 K (1630°C) was obtained on the sample 

at a current of 7.2 amp and a voltage of 189 v. 
** A temperature of 1968 K {1695°C) was obtained at 11.8 amp 
and 200 v. 

*** distance between the turns, 0.4 mm. 


The hollow cylinder under test consisted of seven pairs of 
semi-circular rings, the middle pair being the sample (Fig. 10). 
In the "green" sample, channels were cut for thermocouples 








Fig.lO.The sample for in vacuo measurement up to a temperature of 170(fiC. 

(platinum vs. platinum- rhodium, or tvingsten vs. molybdenum- 
aluminum) and a shaped passage was provided for the pyro- 
nneter leads for measuring the temperature gradient. The 
thernnocouple positions and all the required distances were 
determined either by X-ray photography or, with lesser accu- 
racy, by direct measurements. The heat input power was 
computed from the current and the voltage drop. 

The thermal conductivity-temperature relationship of 
several refractory oxides, in pure condition, was determined, 
at high tennperatures in vacuum, by the modified apparatus. 

The samples were prepared by pressing and then burning 
off the binder material. Measurements up to 1973 K (1700°C), 
using the wire heater, were found extremely accurate because 
of the negligible end losses. It is to be noted that in vacuum, 
each contact surface between the half rings has a very high 
thermal resistance, due to which heat losses from the ends 
become much less in vacuum than otherw^ise. 


The simplicity of measurement and the high accuracy 
obtainable make the wire heater method suitable for measuring 
thermal conductivity of pure oxide materials (zirconium dioxide, 
aluminum oxide, nnagnesium oxide, etc. ) under vacuum, up to 
1973 K (1700°C). Temperatures more than 1973 K (1700OC) at 
the hot face of zirconium dioxide or alumina samples could not 
be obtained, because the corundum former fused and also under- 
went deformation under its own weight. For more conducting 
materials (graphites, carbides, nitrides, borides), a tem- 
perature of only 1673 K (1400°C) could be obtained at the hot 
face by using the wire heaters. 

The m.iniature apparatus (Fig. 11) (with dimensions of the 
sample: 65 mm high, outside diameter 30 to 35 mm, internal 
diameter 10 to 10.5 mm zmd length- diannetejr ratio of 2:1) is a 
variation of the apparatus described above. The small length 
to diameter ratio is compensated by thermal end insulation. 

Fig. 11 Apparatus of small dimensions far determining thermal conductivity 
of small samples. 

1 - tubular former; 2 ■• heating wire; 3 - asbestos cement packing; 
4 - base; 5 - sample; 6 - thermocouples; 7 - refractory ceramic insu- 
lation layer; 8 - asbestos layer. 

The thermal conductivity values of an extremely light 
refractory and of commercial forsterite, measured on the 
miniature apparatus, do not differ from those determined on the 
standard apparatus within the limits of experimiental errors 
(Table 5). Such a miniature apparatus could be used for quali- 
tative measurement of thernnal conductivity for the quality 
control of heat insulating refractories. 



Thermal conductivity of an extremely light refractory material and on 

commercial forsterite 

Extremely light refrac- 




* average 

^average X.l^cal/m h.K 

>pccal/m. h. K 


. >>tcal/m.h.K 

•* (Watt/m. OC) 


(Watt/m. OC) 
2.52 (2.93) 


Tj(Watt/m. °C 

125 0.19(0.22) 

1.6 (1.86) 

230 0.17(0.19) 


1.76 (2.05) 


1.6 (1.86) 

395 0.19(0.22) 


2.06 (2.4) 


1.54 (1.79) 

505 0.20 (0.23) 


2.01 (2.34) 


1.56 (1.82) 

655 0.23 (0.27) 


1.92 (2.22) 



790 0.25 (0.29) 

4. Measuring Th ermal C onductivity up to the Melting 
Points of Highly Re fractory materials -- Z673 K 

The contents of Sections 2 and 3 w^ere taken into considera- 
tion while choosing the method and design of apparatus for evolv- 
ing a unified series of apparatus and comparable methods for 
determining thermal conductivity under a wide range of tem- 

The setup for conductivity measurements of refractories 
up to 2673 K (2400°C) consists of four main systems: 

1. the apparatus for determining conductivity; 

2. the vacuum system; 

3. the power supply; 

4. the measurement system for power and temperature. 

Apparatus for The rmal Conductivity Determination 

Fig. 12 shows the apparatus placed inside a vacuum cham- 
ber. The casing of the apparatus is a 595 x 490 x 250 mm 
parallelepiped of 25 mm angles, which can be taken out of the 


Fig. 12 Apparatus for determining conductivity of highly refractory materials 
in vacuum, up to temperatures close to their melting point. 

1 - vacuum, chamber; 2 - copper bus -bar; 3 - asbestos -cement pack 
ing; 4 - casing; 5 - screen; 6 - copper electrode; 7 - graphite elec - 
trade; 8 - molybdenum box casing; 9 -guards; 10 - sample; Jl - 
heater; 12 - support; 13 - zirconium dioxide plate; 14 - bolt; 15 - wire 
for recording voltage drop; 16 - leads of laminated copper sheets. 

chamber along with the whole apparatus after disconnecting the 
mains. A portable casing is convenient for mounting and 
repairs, because the electrodes and the screens could be 
connected outside the vacuum chamber. Steel supports 12 and 
asbestos cement packing 3 are fixed to the lower plate of the 
frame. The current-carrying bus bar 2 lies freely in the pack- 
ing. Similar packing and bus bar are attached to the top plate. 
The first of the screens 5, made of 2 nnm iron sheet, is attached 
to the frame. 

The electrodes, which fix the heater, consist of copper 
bus bars 2, to which a graphite split contact 7 is screwed in with 
two steel bolts. The graphite plate is pressed on to the heavier 
graphite mass with two bolts, thereby keeping the heater 1 1 in 
position. The upper electrode is firnnly attached to the copper 
bus bar with a bolt and the lower one hangs freely on the heater. 
Bolt 14 fixes the lower electrode only at the time of mounting 
the heater. The free hcinging of the lower electrode compensates 
for the thermal expansion of the heater. 


Electric current is led in through the large vacuum inlets 
to which the bus bars 2 are connected through leads of laminated 
copper sheets. 

The radiation-shield system consists of a first layer of 
flat shields of 2 mm iron sheet fixed on the frame, a second 
layer of flat shields and a third layer of cylindrical ones, each 
made of 1 mm. sheet iron. The second layer of radiation 
shields is attached to the upper and lower plates of the frame 
and semicircular shields are attached to the front and back 

Graphite tubes and 5 mm tungsten w^ire serve as heating 

The graphite heater not only enabled the use of the same 
samples which were used for the wire heater method, but made 
it possible to obtain considerably higher temperatures [2373 to 
2473 K (2100 to 2200°C) ]. It is very strong, but at high tem- 
peratures, graphite vaporizes considerably, thereby dirtying 
the samples and reacts with some of the materials under investi- 
tation (for example with zirconium dioxide at 22 00 to 2400°C) to 
form carbides. 

A tiingsten heater makes the samples less dirty, and reacts 
less w^ith the test materials. But the electrical resistance of 
tungsten wire is about half that of graphite, which causes a 
number of technical difficulties in obtaining high temperatures. 

While conducting the tests, both types of heaters were 
used, though, as a whole, the tungsten wire heating w^as more 
successful. It is also to be borne in mind that the cross section 
of the graphite heater is about 10 times that of tungsten wire and 
so the heat losses along the heater axis for tungsten would be 
less, even after accounting for the difference in thermal conduc- 

Owing to the small diameter of the tungsten heater, the 
outside and inside diameters of the test cylinder (Fig. 13) and, 
consequently, the heat losses through its ends could be reduced. 

The influence of the cross section area on the accuracy of 
measurement was determined experimentally, by using graphite 
samples of different outside diameters. It appears from Fig. 14 




Fig. l3.Sample far measuring thermal conductivity up to the;, melting point of 
highly refractory materials (2000 to 2500OC). 

10 \ 

W 3D- 

A '" 


::? 10\ 

rt 30 

O 10 

X to- 




"2 — * a — ^a- 

-«— ii 

> ^U I'' ijH'^a 


♦ ft5 « 
3V J • 
73.3 6 



1073 ~^" li73 ' 1*73 ' 1613 ' !813 2073 2273 2*73 
(800) (WOO) (1200) lltOO) (1600) (1600) (2000) (2200) 

Temperature K (OC) 

Fig. 14. Thermal conductivity of graphite electrodes during tests on cylinders 
of different diameters. 

1 2 3 4 

outside dia, , mm 20 30 40 50 

cross section area, mm' 


706,5 1256 1962.5 


that, for a certain cross section (outside diameter less than 
40 nun), good reproducibility was obtained in the entire tem- 
perature range; but for larger sections (outside diameter 40 to 
50 mm), and particularly at temperatures 1773 K th6 thermal . 
conductivity values were somewhat higher at higher heat inputs. 

The test cylinder, consisting of six guards 9 (Fig. 12) and 
one sample 10 in the middle, is mounted aifter the heater is 
fixed in position.* The guards and the sample have the same 
heights, same outside and inside diameters. They should also 
have nearly the same conductivity. 

The semicircular rings of the test cylinder are so set that 
the gaps between the semicircular rings lie crisscross (to 
reduce the radiation losses from the heater) and the tem- 
perature sensing holes in the sample and heater are situated 
along the vacuum chamber axis to facilitate temperature read- 
ings through an observation window in the chamber. 

On the cold face side, the cylinder is surrounded by a 
split box 8 made of molybdenum strips with tungsten coverings 
at the surface of contact with the cylinder. The. casing is filled 
with porous greinules of zirconium dioxide*. Up to the highest 
temperature of investigations (2300 to 2400°C at the hot face of 
the sample, 2100 to 2200°C on the side facing the casing) such 
a casing did not fail even once during use and remained alnnost 
intact, without any deterioration during working**. 

The vacuum system consists of a vacuum chamber of 
0. 5 m^ volume, high vacuum diffusion pump of 1000 -v /sec 
capacity, fore -pump Type VN-1 and vacuum mains. Such a 
large vacuum system enables to exhaust up to 1 x lO""* mm- 
HgCol in the whole tennperature range and to maintain the high 
vacuum during all the measurements. Vacuum control is done 
continuously by vacuum-meters fitted w^ith pressure control 
lamp (vacuostats). 

*The technology of preparation and the filler material were developed by 
A. A. Pirogov [6], who provided us with the necessary quantities of the 
powder for vacuum experiments. 

**Other possible screen -casings were also tried. Lightweight high-alumina 
refractory works satisfactorily up to 1500PC; at higher temperatures ^ther - 
mat deterioration and gas occlusions are observed. Heat treated zirconium 
dioxide used for the casing has sufficient refractoriness but low endurance 
(i.e., its insulation breaks down by prolonged heating). 


The electrical power system comprises a primary trans- 
former. Type AOSK 25/0.5 of 25 kw, capable of insuring smooth 
change of voltage from to 250 V at a working current of 110 
amp, and a secondary power transformer. Type TPO-102 of 
10 kw (maximum current 800 amp. at 12 V). The current was 
measured with the help of current transformers of precision 
class 0. 2 (Type UTT-5 for up to 600 amp. , UTT-6 above 
600 amp. ), and the potential drop was measured with the help 
of voltmeters of precision class 0. 5 having low power consump- 

The temperature drop was measured with the help of 
thermocouples. Athigh temperatures and in electrically conduct- 
ing samples, it was measured with an optical pyrometer through 
an observation window on the cover of the vacuum chamber. The 
absorption loss through the 5 mm thick glass piece was deter- 
mined, at the time of measuring the tennperatures, in several 
ways: with a standard pyrometer strip lamp, on a foil of 20% 
RhPt in air, and on a graphite heater by superposing aaiother 
observation glass. The mean values of the corrections applied 
for the absorption are given in Fig. 15. 


























1073 1Z73 mS 1673 1873 2073 2273 2173 
(800) (WOO) (1200) (lliOO) (IBOO) (1800) (2000) (2200) 

Temperature K (^C) 

Fig. 15. Absorption correction for the glass, fox tgfnperature measurements 
with optical pyrometer. 

Thermal conductivity at 2673 and 22 73 K was measured in 
vacuum and in atmiospheres of nitrogen cind argon. The maxi- 
mum temperature was reached by putting on power at not more 
than 10 kw. 

The mean square deviation of the results, which shows the 
reproducibility of measurements, lies between 2.5 to 5% for 
low conducting samples ( 1 to 3 kcal/nn. h. K. , i. e. , 1. 16 to 


3.5 Watt/m. K) and 10 to 15% for highly conducting samples 
(10 to20kcal/m. h.K. , i.e., 11. 63 to 23. 3 Watt/m. K). 

The time required for an investigation on the temperature— 
thermal conductivity relationships, of a sample, from 1173 K 
(900°C) to the maximum temperature -- taking measurements 
at about 8 points, and including the time for loading and pumping 
out the air --is 7 to 8 hours. 

A comparison of the results obtained by using wire heaters 
up to 1973 K (1700°C) (Section 3) and those obtained by using the 
tungsten and graphite heaters shows that under a given set of 
conditions of the test cylinder and thermal conductivity, the 
values of thermal conductivity obtained with graphite and tung- 
sten heaters are higher. Considerably higher (above 40%) values 
were found in the case of low conductivity materials (of the order 
of 1 kcal/m. h. K), amounting to an increase of about 15% for 
materials having thermal conductivity 4 to 5 kcal/m. h. K (4. 65 
to 5.81 Watt/m. K). For higher conductivity materials (graphite, 
zirconium diboride, etc. ), the difference was within experi- 
mental errors. 

The abovementioned increase in conductivity values for low 
conductivity materials is reduced as the temperature increases 
and as graphite heaters are substituted by txuigsten heaters. The 
latter have a lesser cross section of test cylinder than the 
graphite ones. 

The difference in the conductivity values obtained on differ- 
ent apparatus could be explained on the basis of different amounts 
of heat disspation at the heater surface. For wire heaters, the 
heat losses through the 0. 9 mm diameter wire along the un- 
cooled surface amd along the former of the heater are very small 
compared to the heat dissipation of rod-heaters through the large 
water-cooled graphite and copper electrodes. 

When the thermal conductivity of a sample is approxi- 
mately equal to that of the heater (graphited materials, car- 
bides, boridqs, nitrides), the heat flow is radial. The heat flow 
along the length of the heater being negligible (due to the differ- 
ence in the path length for heat flow), there is good agreennent 
in the results for highly conducting materials. The cross sec- 
tion of the heater should be reduced and its length increased, in 
order to minimize the heat transfer along the heater axis. 


Therefore, the method described above, specially developed for 
high teirqjerature-cum-vacuum measurements with large tung- 
sten and graphite heaters, should be used only for studying the 
thermal properties of materials whose conductivity is more than 
10 kcal/m. h. K. For materials with lesser thermal conductivity, 
the errors in this method are quite large. 

Let us now estimate the maximum theoretical error of 
measurements at high temperature under vacuum. 

As shown earlier (2), 

^ = [^ -t^-t ^Ii:L^ 

The degree of accuracy of the instruments used (the volt- 
meter and the ammeter -with its current transformer. etc. ) w^as 
such that: 


V - -'7 ' 

A%=^'%.= 0.5 mm; A. i is the accuracy of length measure- 

For the selected sample dimensions and accounting for 
deviations from the nominal positions of individual holes: 

-\ = 5. 5 to 8. 1 mm; 
^1= 17.2 to 24. 1 mm; 
'£rv-^= 0.83 to 1. 19. • 

Substituting all these values, the errors in length measure- 
ments come to 10. 3%. This relatively high error is due to the 
small dimensions of the sample. 

The errors in temperature measurements depend on the 
thermal conductivity of test miaterials and on the temperature 
concerned (Tables 6 and 7). 




Relationship between the temperature drop (T2- Tj) and thermal conductivity of the material 

at various test temperatures 

Thermal cond. 
kcal/m. h. K 
(Watt/m. K) 

Temperature drop (T2 - Tj) 

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 
(1173) (1273) (1373) (1473) (1573) (1673) (1773) (1873) (1973) (2073) (2173) (2273) 


Zirconium di- 
oxide, zirco- 1-2 
nates (1. 16-2. 3) 

Spinel, oxide of 4-5 , 

aluminumi (4.15-5.82) 

nitrides, 10-20 

silicides (11.63-23.3) 

nitrides 22 (25.6) 15 



195 220 - 260 < 315 370 - - 475 
75 90 115 145 185 220 250 285 - 340 

75 100 


25 30 40 55 60 

75 90 



Dependence of percentage errors in temperature measurements using an optical pyrometer of an 
accuracy of + 5 K, at different test temperatures of various types of materials 

Thermal cond. „ , ^ 

kcal/m.h. K Percentage error _ _ , % at test temperature*, °C (K) 

Material (Watt/m. K) 

T, - T, 

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 
(1173) (1273) (1373) (1473) (1573) (1673) (1773) (1873) (1973) (2073) (2173) (2273) 




1-2 (1.16-2.3) 


Spinel, oxide 


of aluminum 

4-5 (4.15-5.82) 













2.56 2.27 - 1.92 - 1.85 1.35 
6.7 5.6 4.35 3.45 2.70 2.25 2.00 1.75 

6.65 5.0 



20.0 16,5 12.5 9.1 8.3 

6.7 5.45 



The maximum theoretical error in this high temperature, 
method for thermal conductivity measurement depends on: 

a) error in length determinations (+10.3%)- 

b) error in power determination (+!%)•, 

c) error in temperature measurements (which depends on 
conductivity of the material and on temperature). The errors 
are as follows: for material with high thernnal conductivity 

[50 kcal/m.h. K (58. 1 Watt/m. K) at 1173 K (900°C) ] 66%; for 
material with thermal conductivity around 2 kcal/m. h. K (2. 33 
Watt/nm. K) at the highest temperatures, 2%. 

The mean square deviation of the results: for samples with 
thermal conductivity 2 kcal/m. h. K (2.33 Watt/m. K), 2 to 5%; 
for samples with conductivity 10 to 20 kcal/m. h. K (11. 63 to 
23.3 Watt/m. K), 10 to 15%; for samples with thermal conducti- 
vity 50 kcal/m. h. K (58. 1 Watt/m. K), 12 %. 





1 . General Characteristic of Refra ctories fron^ the Heat 
Exchange Point of View 

Refractories, i. e. , materials with high melting points, 
are w^idely used in science and technology. Thus, refractory 
metals of high melting points (tungsten, tantalum, molybdenum, 
niobium), substances with conductivity similar to metals (car- 
bides, nitrides, graphite, carbon dioxide), semiconductors 
(chromium oxide, zirconium dioxide) amd insulators (insulating 
oxides, zirconates) -- all these could be classified as refractory 

Multicomponent systems (solid solutions, and multiphase 
systems), as well as single-phase, single-connponent systems 
are used. A refractory can have crystalline (crystalline quartz) 
or amorphous structure (quartz glass). 

The following oxides form the main components of refrac- 
tories both in pure form and in compounds and solid solutions: 

BeO, MgO, CaO, ZnO, NiO, FeO, BaO, MnO, CoO, SrO, 
UO2, Ti02, Th02, Zr02, Si02, Hf02, Ce203, Sn02, Cr203, 
Fe203, La203, Ga203, Y2O3, V2O3, Ta205, AI2O3. 

MgO. AI2O3 (mineral spinel); Zr02.Si02 (zircon); 
3AI2 03.23102 (mullite); 2MgO. Si02 (forsterite) are the more 
common chemical compounds in use. 

The heat transfer in a hard crystalline substance is 
brought about by elastic oscillations of the lattice (lattice ther- 
mal conductivity) and conductance electrons (electronic thermal 
conductivity) and in the case of porous semiconductors by the 
diffusion of pores. 


A. F. loffe [7] showed that in the case of metals and semi- 
conductors, the electronic and lattice parts of the thermal 
conductivity of the solid are additive, i. e. , 

A = ^lattice + A electronic . (6) 

The proportion of each of the components in the total 
conductivity is different, depending on the electronic structure 
of the solid material. In metals, the concentration of conduct- 
ance electrons is o£ the order of 10 vcrrr. Hence for chromium- 
nickel steels with low percentage of additives [8] the electronic 
conductivity part is 77 to 89% of the total conductivity. In addi- 
tion, the conductance electrons facilitate dispersion of elastic 
v^aves in electrons, i. e. , they also influence the lattice conducti- 
vity indirectly. 

Roughly speaking, the influence of electrons on thermal 
conductivity is about twice that of the elastic oscillations of the 

It has been shown by V. E. Ivanov and V, V. Lebedyev [9j that 
for W, Mo, Cu, Au at room temperature, '^lattice (phononic) 
constitutes 10 to 20% of A measured' ^^'^ ^^ ^^^ *° ^^^ ^ 
(400 to 500°C) ^ lattice ^^ considerably smaller in percentage. 

The electron concentration in semiconductors is lO'^'^/cm^, 
i- e. , X measured approximately equals X lattice- ^°^ 
example, electronic thermal conductivity of zirconium dioxide, 
a refractory semiconductor of small resistance, reaches only 
0. 2% of the total conductivity at considerably high temperatures 
(2073 K,i. e.,1800OC). 

Refractory oxides are either insulators or semiconductors. 
The more common refractory oxides are mainly insulators: 
MgO, BeO, AI2O3, Si02, Th02 . Consequently, the laws govern- 
ing variations in thermal conductivity in such materials are 
determined by the conductivity of the lattice. 

Experimental results of investigations on the laws of 
thermal conductivity of refractory insulators and of the various 
crystalline modifications, which are commonly met with in 
refractory practice and in the investigations of temperature 
relationships of the conductivity of insulators above the charac- 
teristic temperature (right up to the melting point of selected 
materials), are given in this chapter. 


2. Relation Between Thermal Conduct ivity; of Refractory 

Insulators a nd Temperature 

The sannples were made of pure materials during these 
temperature-thermal conductivity studies. They had low poro- 
sity, in order to practically eliminate the effect of pores. 

Measurements were conducted in a w^ide temperature range 
extending up to the pre-melting region. 

Investigations on polycrystalline AI2O3, prepared by 
pressing from fine powder (less than 2 microns), with an 
open porosity of 0. 02 to 0.56% and a mass-density 3. 76 to 
3. 80 g/cm3, showed that thermal conductivity is reduced in the 
temperature range 773 to 1073 K (500 to 800 °C) and that with 
further increase in temperature, it remains constant within 
+ 10% (4. 5 kcal/m. h. K) up to the highest temperature experi- 
mented with (I993 K), It appears from the ( *■ ) vs. T relation- 
ship (Fig. 16) that in the temperature range 773 to 1073 K 
(500 to 8OOOC) the variation oi { A. ) — . T is quite regular*. 


Since the character of the A (T) function has a basic 
importeince, avoidable inaccuracies in high temperature investi- 
gations were eliminated by measuring the temperature drop by 
suitable methods, e.g. by thermocouple and electric pyrometer 
(on cold face) and thermocouples (on hot face). It should be 
emphasized that no increase in thermal conductivity was noticed 
after reaching a minimum value. However, some differences 
were observed on conaparison with the values obtained by the 
hollow ellipsoid method [H]. The minimum values of absolute 
A for AI2O3 [19] are close to one another (in Fig. 16), though 
they are attained at high temperatures (1473 to 1673 K). The 
main difference is that McQuarrie [10] noticed an increase in 
the thermal conductivity at 1673 K, but in the experiments des- 
cribed here,the conductivity remained constant almost up to the 
melting point. The accuracy of measurements being greater 
now than in [11], it can be surmised that the increase in thermal 
conductivity of AI2O3 noticed in [10] was caused by some appre- 
ciable experimental errors, and by the arbitrariness adopted in 
passing the curve through the experimental points. It should be 

*Tke deviation in the thermal conductivity values from those of published 
data [3] could, according to us, be attributed to the difference in the purity 
of sample. 


noted that other authors [12] also did not record an increase in 
thermal conductivity at pre-melt temperatures. 

373 513 113 913 1113 1373 1573 1773 1973 
1100) 1300) (500) noO) 1900) (1100) (1300) (HOB! (1700) 

Temperature, K (°C) 

Fig. le.Variation of thermal resistance of polycrystalline AI2O3 with tem- 

1 -author's data; 2 - data of Kingery et al [3j. 

Thermal conductivity measurements of polycrystalline 
magnesium oxide o£ zero porosity revealed two regions (Fig. 17) 
Twith different relationships between temperature and conducti- 
vity: the range 1173 to 1573 K (900 to 1300OC), in which the 

X'>-'— ; relationship holds good, and the range 1473 to 2023 K 

(1200 to 1750OC) in which thermal conductivity remains 
consteint •within 4% (which is better than the accuracy of the 
method). For further verification of the nature of variation w^ith 
tennperature, experiments were conducted at still higher tem- 
peratures. Measurements in an argon atmosphere did not 
reveal an increase in the conductivity up to 2223 K (1950OC), 
the temperature at the internal surface of the sample being about 
2323 K. Similar results were obtained for MgO with 2.5% 

373 573 773 973 1173 1373 /573 1773 1973 
(100) (300) (5001 1700) (900) (two) (1300) (1500) (1700) 

Temperature, K (°C) 
Fig. IT.Variation of thermal resistance of polycrystalline MGO with tem- 

1 - data of the present investigation; data of Kingery et al [3j. 


An increase in thermal conductivity was also noted in [10] 
for BeO at temperatures above 1473 K. Though the present in- 
vestigations did not include BeO, it is appropriate to note that 
recent measurements on BeO and on a mixture of BeO with 1% 
Al up to 23 73 K [13] showed an increase in thermal conductivity, 
only at temperatures higher than 2073 K. 

It should also be pointed out that high temperature measure- 
ments for uranium dioxide [14] did not show a minimum value of 
thermal conductivity up to 23 73 K. 

Thus, there is a group of substances {AI2O3, MgO, UO2) 
in refractory insulators, which have the following peculiarities: 
there exists a very high maximum value of conductivity in the 
lower temperature region; the ■X~i relationship holds good 

from the Debye temperature up to 1273 K (AI2O3, MgO), 2173 K 
(BeO), 2373 K (UO2); a minimum value of ^ is obtained at high 
temperatures, due to the mean free path of phonons becoming 
comparable to the interatomic distances in the crystal lattice. 

The increase in thermal conductivity after reaching a mini 
mum, which was interpreted as a definite law by some authors 
[15, 10, 16, 17] appears controversial, as also all the explana- 
tions given for this phenomenon. The materials discussed here- 
in are characterized by quite high Debye temperatures (800 to 
1000 K). 

Measurements on quartz (Fig. 18) in the temperature range 
up to 1773 K on the hot face (average temperature 1400 K) show 
that another variety of substances exists among refractory insu- 
lators, for which thermal conductivity has an increasing charac- 
ter throughout the temperature range of 2 73 K (0 °C) to tem- 
peratures close to their melting point. However, for crystalline 
quartz, thermal conductivity increases only after it has attained 
a minimum possible value, which corresponds to the mean free 
path of phonons, and is comparable with the interatomic dis- 

The temperature- conductivity relationship for quartz, Ln 
a wide range of temperatures (from 4 K to the melting point), has 
the following peculiarities: a low maximum for thermal conducti- 
vity ( "^max ^°^ quartz is about one-sixth of that for AI2O3); the 
range of minimum values of conductivity lies around 473 K; the 
thermal conductivity increases from 373 K (Fig. 18) up to the 



A 0.8 




1*73 l$73 

(»m (1100) 

Temperature, "C 
Fig. IS.Temperature'- thermal conductivity characteristic of polycry^talline 
quartM (1) and quartz glass (2). 

melting point; for quartz, ^max occurs at 10 K (compared to 
50 K for AI2O3 and 110 K for MgO), and the Debye temperature 
is around 250 K (compared to 700 K for MgO and 750 K for 

At temperatures above 273 K (0°C), a similar pattern is 
observed for polycrystalline zirconium dioxide (Fig. 19) and for 
calcium, barium and strontium zirconates (Fig. 20) in the ther- 
inal conductivity — temperature relationship. 

^ to 






1213 1H13 1673 1873 2073 2273 2173 2673 
(WOO) (1200) (1100) (mO) (1800) (2000) (2200) (2*00) 

Temperature, K (OC) 



Fig. IS.Temperature — thermal conductivity relationship for polycrystaUint 
zirconium dioxide. 


US 3,2 
S 2.* 


3.7 id 




yc "IS 1073 1573 1773 1973 2173 

<^ (300) (1 too) (1300) (1500) (1700) (1900) 

Temperature, K (°C) 
Fig. 20. Temperature — thermal conductivity relationship for zirconates. 
1 - strontium zirconate (SrZrOj); 2 - calcium zirconate (CaZrOs); 
3 - barium zirconate (BaZrOs). 

3, Thermal Con ductivity of Refractories Formed by 
Combinations of AI2O3 and Si02 

Al2 03-based refractories are widely used in industry. The 
AI2O3 content varies ■widely -- from 100% (corundum) to 30 to 
35% (fire-brick). Silica Si02 is the second major constituent. 

Thermal conductivity of several materials with different 
AI2O3 and Si02 contents was determined in order to study the 
law^s of variation of thermal conductivity in the Al2 03-Si02 

Figs. Zl and 22 show the experimental curves of the ther- 
mal conductivity — temperature relationship, for dense and 
porous materials. Some properties of the investigated materials 
are given in Table 8, -while experimental values of thermal con- 
ductivity are shown in Tables 9 and 10, 

Thermal conductivity variation curves, depending on the 
AI2O3 content^are shown in Fig, 23 (for dense materials^) and 
Fig, 24 (for porous materials). 

In the binary system Al203-Si02, the laws of variation of 
therinal conductivity are applicable to only dense alumina- sili- 
cate materials, after applying corrections for the presence of 
additives and for non-zero porosity (see Figs, 21, 23), In the 
porous ceramics of the AI2O3— Si02 system, the laws obtained 
are distorted due to porosity and are considerably dependent on 
the distribution of pores according to size. 

^Here dense material means a material with porosity up to 20 to 25%, for 
which simple computation to zero porosity is valid. 


Some properties of alumina- silicate materials 


Chemical composition, % 
AI2O3 SiC)2 ^6303 CaO MgO 

Packing Apparent Water 
Mineralogical density porosity permeability 

composition g/cm^ % nj/min* 




Kaolin (from 

Blast furnace 




1.00 0.18 0.10 0.44 Sample consists 2.96 24.0 

essentially of 
High alumina- 83.19 13.6 0.46 0.6 0.58 Corundum 80%, 3.06 9.4 

vitreous substance 
15 to 18% 

82.84 13.7 0.56 0.61 0.50 - Not 10.0 .1.72 


77.6 17.0 

72.98 23.22 0.84 0.75 0.72 Corundum, mul- 2.55 16.5 3.71 

lite 80%, vit- 
reous substance 

68.3 25.1 0.70 0.75 1.80 MuUite, corundum 2.51 


42.9 52.7 0.92 0.60 0.57 Mullite, corundum 2.38 12.4 

53%, vitreous sub- 
stance 47% 

35.9 58.3 1.26 0.59 0.72 Mullite, corundum 2.10 

37%, vitreous sub- 
stance 63% 
High alumina. 81.0 16.54 0.36 0.46 0.50 - 1.40 55.8 64.12 

16.5 3.5 


15.1 4.5 


♦Water permeability m.ean8 the rate of penetration of water under a certain pressure through a certain thickness 
of the sample. 


Thermal conductivity of dense refractories of the AI2O3 - Si02 system for various temperatures 
(Calculated for zero porosity by the formula: X, = >\ (1 - p) 

Chemical comp 




3rmal conductivity, kcal/m. h. 

K at test 







°C (K) 

Refractory type 




800 1000 
(1073) (1273) 




1. 00 








High alumina content 














3. 11 

2. 18 















25. 1 








Kaolin (from Novo- 











Firebrick (blast 











AI2O3 [3] 











Natural quartzite 













Thermal conductivity of porous lightweight^ refractories of the A.1203 - Si02 system 

Chemical compo- 

- The 

rmal c 

onductivity. kcal/m. h. 

K, at 





sition % 

temperature K 


Microstructure (Petro- 










graphic analysis) 







Corundum, light- 

Pores round, closed; 











dominant sire 0. 3 to 
0. 9 mm, rc»x 3 mm 

Corundum light- 

Pores round, closed; 











dominant size 0. 6 to 


1.4 mm, max 1.6 mm 

High alumina, 










Pores round, closed; 











dominant size up to 
1. 2 mm 

Firebrick, light- 

Pores of irregular ihape. 











0.3 to 0.9 mm, open, 
max. size 1.5 mm 

Firebrick, ultra- 

Pores round, closed. 











dominant size 0. 1 to 
0.2 mm, max. 0.4 mm 

Dinas lightweight 










Pores of irregular shape, 
closed; dominant size 
0.3 to 1.2 mm; max 
2.5 mm 















t< at 

J7J J7J 77J «7J >t73 1373 1173 
(IfO) (300)1500} (700) (S00)(im)0300) 

Temperature, K (°C) 

Pig. 21 .Temperature -thermal conductivity relationship of refractories of the 
AI2O3 — Si02 system (materials with a porosity at which computa- 
tion to zero porosity is valid). 

12 3 4 5 

AI2O3 content, % 97. 82.2 63.3 45.0 37.35 

Apparent porosity, % 24 12.7-13.5 16.5 12.4 15.1 


2.4 r 

;5 J.2 
-^ Ofi 



2.3 t^ 

m ^ 


~*7J fiw 873 /m 1213 nis' 

(200) (m (600) (800) (1000) (tlOO) 
Temperature, K (°C) 

Fig. 22. Temperature — effective thermal conductivity relationship of the 
^^2^3 ~ Si02 refractories (porous materials). 

12 3 4 5 6 7 

AI2O3 content, % 95.4 95.9 81.0 44.4 31.2 35.73 1.75 
porosity, % 80 82,5 55.8 70 59-3 88 


*Lightweight Dinas 


Since all parameters could not be insured to be identical 
due to technological difficulties, the thermal conductivity data 
for the samples of alumina- silicate materials (Fig, 22 to 24) are 
only particular cases from the point of view of the study of the 
binary system. • 

10 X M TO X 

AI2O3 % (Wt. ) ^^°2 
Fig. 23.Curve showing variation of 
thermal conductivity with 
concentration of consti - 
tuents of refractories of 
the AI2O3 ~ Si02 system 
(dense materials) at 
20(PC (473 K). 

Fig. 24. Relationship of thermal 
conductivity with con- 
centration of constituents 
of refractories of the AI2O3 
Si02 system (highly porous) 
(the numbers on the curve 
indicate porosity). 

A reduction in thermal conductivity with an increase in the 
SiOo content is observed in dense alumina- silicate materials 
(Fig. 23). The reduction is especially sharp under relatively 
very low silica concentrations (5% by weight Si02). With further 
increase in silica content, thermal conductivity of the system 
decreases continuously throughout the concentration range. 

Marked difference (of more than one order of magnitude) 
in thermal conductivities of the pure components is charac- 
teristic of the AI2O3 - Si02 system. At 3 73 to 4 73 K, the low 
conducting components have the minimum possible thermal con- 
ductivity values, which correspond to mean free path of phonons 
and are comparable in magnitude to interatomic spaces. This 
peculiarity results in an unsymmetrical concentration curve, 
which is different from the usual U-curve observed for compo- 
nents of equal thermal conductivity [18, 19]. For highly porous 


materials (Fig. 24) also, the unsymmetrical concentration curve 
is possible, but appreciable difference in porosity is noticed and 
calculation at zero porosity is not reliable. 

A sharp change in the temperature characteristic is also 
noticed in the AI2O3 system. While studying the causes for such 
a change, it is necessary to consider the mineralogical changes 
that take place in the system with various AI2O3 and Si02 con- 

Table 8 gives the results of petrographic studies on 
samples. With a decrease in AI2O3 content and simultaneous 
increase of silica, the corundum content of the sample is reduced 
because of muUite formation (3AI2O3. 2Si02). A part of the 
silica forms a vitreous substance. 

For example, with 83. 19% AI2O3 (13. 6% Si02), a micro- 
scopic examination of the sample revealed 15 to 18% vitreous 
substance ajid 1 to 2 % muUite. In the concentration range 70 to 
85% AI2O3, a large quantity of mullite (65%) was formed, while 
the vitreous substance remained constant. With further increase 
in Si02 content, two phases were revealed in the sample, viz. , 
nnullite and vitreous substance. 

Similar phase changes were observed by V. A. Kopetkin eind 
D. N. Poluboyarinov [2 0]. Chemical analysis show^ed that the 
quantity of the vitreous substance phase increased at •^ 77% 
AI2O3. X-ray investigations showed that for pure materials^ the 
vitreous substance phase appears earlier ( ■<C. S5% AI2O3) than 
for industrial materials ( -eC^ 75% AI2O3). 

Thus there can, in general, be three phases in the AI2O3 — 
Si02 systenrs samples, namely, mullite, corundum and vitreous 

From the diagram, it will be seen that one of the phases 
exists in negligible quantities and so in practice there are only 
two phases: corundum — glass or, mullite — glass. The 
mineralogical connposition determines the change in the charac- 
ter of the tennperature relationship. For AI2O3 and mullite, 

i "^ 

A' — ' '^ ', for the vitreous substance, 7^ ^-vj T . The thermal 

conductivity of AI2O3 is about 1. 5 times that of mullite. 


In general 

where Ci, C2, C3 are concentrations of corimdum, mullite, and 
glass respectively. 

and a, b, d are constants, a ];> b 

Since with changes in AI2O3 and Si02 concentrations the 
phase composition changes in the sequence: corundum ->^ glass— > 
mullite, the values of the terms in (7) also change. Hence with 
an increase in silica content the temperature— conductivity- 
relationship changes from A/' — '±-— to \^-^ T. 

T ^ 

4. Thermal Conductivity of the System: Crystalline Silica- 
Quartz Glass 

Quartz glass refractory is quite commonly used in industry. 
It is well known that at a certain temperature quartz crystallizes 
into crystobalite [Zl to 24]. The temperature and time required 
for complete crystallization at a given tennperature depend on the 
mass of the sample, time for temperature rise, etc. 

The crystalline phase sets in, in the glass-cracks and 
around the pores, in the form of metastable crystobalite. Later 
on, this transforms into stable crystobalite and spreads in all 
directions from the origin of the cyrstalline phase. 

Closed pores open out during crystallization, and at 1673 K 
all the pores become open. Along with this, the porosity is in- 
creased to some extent. The incremental change in porosity is 
of course small, of the order of a few percent. Thus, the 
structure of quartz glass rapidly changes during sustained heat- 
ing (this also happens in equipments in which quartz glass is used 
as refractory). Accordingly, it is possible to observe the 
change in the physical properties during the transition fromamor- 
phous to crystalline state as well as in the proportion of the 
amorphous and the crystalline phase in the specinnen. Given 
one specimen of quartz glass, a series of different concentra- 
tions of the crystalline silica, i. e. quartz glass, can be ob- 
tained by sequential heat treatment. 


Thermal conductivity of the two-phase system crystalline 
silica-quartz glass was studied by the author. A cylinder 
(height 90 nam, outside diameter 75 mm, inside diameter 20 ntur) 
was cut out from a quartz glass block and this served as the 
sample for the experiments. 

Sustained heating of the sample was done in a cryptol fur- 
nace — initially at 1673 K, and later on at 1773 and 1873 K to 
accelerate the crystallization process. After each heating, a 
small test piece of the sample was subjected to petrographic and 
3{-ray analysis. 

The quantity of crystobalite and variations in the micro- 
structure during crystallization w^ere checked by petrography 
(Table 11) and by the line intensity (111) of crystobalite on ioni- 
zation curves. Fig. 25 shows the growth of crystobalite forma- 
tion with time of heating and temperature. 




Heating tinne, hr. 

J ii 6 8 10 12 III M W 20 27 




Temperature, K (°C) 

25. Relationship between the 
quantity of crystallized 
quartz glass in crystoba - 
lite, time of heating, and 

The variation of thermal conductivity with temperature was 
determined on the same sample, at intervals of 200 K. The 
relationship between the mean conductivity of quartz glass and 
crystobalite content is shown in Table 12 and in Fig. 26. 

Thermal conductivity of original quartz glass (Fig. 27) 
increases negligibly with rise in temperature up to 623 or 673 K 
(350 or 400*C), in a manner similar to that of variations in the 



Variationa in the microstructure of quartz glass during crystallization by 


perature Hold- Pore size*. m m 
of heat , Ing 

°C (K) time, max. domi- 
h. nant 



Quartz tropic, Microstructure 


% foliated characteristics 








Silicates in the 
glass with weak 
in the form of 
small additions 



2 0.32 0.04-0.12 

4 0.24 0.05-0.12 

6 0.32 0.08-0.20 

8 0.80 0.08-0.28 

10 0.72 0.08-0.20 
iZ 0.20 0.04-0.13 
14 0.40 0.05-0.16 

Round 2-3 


Cracks with 




-do- 2 



Round, 1 


Crystobalite in the 

oval and 

form of radial 


rays. Manypores 
and thin cracks 

Elongated, 1 


Cracks withorien- 


tation. Elongated - 


oval pores set in 
one direction 

Round traces 


Cracks in differ- 


ent directionB. 


Cracks with 



orientation and 






0.30 0.08-0.15 









0.60 0.10-0. 20 







* Pores in small numbers 


from X- 

-ray analysis 




Without any defi- 
nite orientation 


Thermal conductivity of the system Si02(crystobalite) - quartz glass, determined on quartz 
glass specimens with different crystobalite content 



conductivity kc 

al/m. h. 

K at mean temperature K (°C) 

of the 

' Hold- 













heat, K 
























































































































































20 <iB sa 
Crystobalite content, % 

Fig. 26 .Variation of ther>nal conductivity 
with concentration in the two- 
phase system quartz glass — 
crystalline silica (crystobalite), 
at temperatures. 
1 - 100(PC (1275 K); 2 ■ 90(PC 
(1173 K): 3 - 80(PC (1073 K); 
4 - 700^ C (973 K); 5 - 60(PC 
(873 K); 6 - 50(PC (773 K); 
7 40(PC (673 K): 8 - 30(fC 
(573 K): 9 - 20(PC (473 K). 

conductivity of high Si02 content materials. (See Section 5, 
Chapter III). With further increase in temperature, the thermal 
conductivity increases rapidly, because the heat flow by radia- 
tion increases due to high transparency of the material. This 
increase in conductivity is so large that at temperatures around 
973 to 1023 K (700 to 800°C) the radiation component of conducti- 
vity becomes most predominant (Fig. 2 7). 

The variation of thermal conductivity of quartz glass dur- 
ing crystallization in different temperature regions is different. 
It also varies with the concentrations. 

The temperature range of measurements can provisionally 
be divided into two parts: 473 to 673 K (200 to 400°C) and 773 to 
12 73 K (500 to lOOOOC) (See Fig. 26). In the first region, both 




/^ «»• 















«7J «7J «7J 7i»7J /?7J 
1200) (HOO) (tool 1100) (lOOOl 

Temperature, K (°C) 
Fig. 27. Variation of thermal conductivity of 
quartz glass with temperature and the 
extent of crystallization. 

1 - amorphous glass; 2 - glass with 
40% crystobalite; 3 - reformed glass 
with 100% crystobalite. 
the components have almost the same thermal conductivity and 
the transition of the concentration curve from the value for 
quartz glass to that of crystobalite is smooth and possesses a 
minimum which is difficult to distinguish. The more rapid de- 
crease in thermal conductivity of quartz glass in the low con- 
centration region can apparently be explained by the fact that at 
these temperatures, a part of the heat is carried by phonons. 
Therefore, even small quantities of the crystalline phase, with 
the cracks appearing therein, reduce transparency of tne 
material, leading to a rapid decrease in the mean free path of 

In the temperature range 773 to 1273 K (500 to 1000°C), 
the two conaponents in quartz glass have quite different thermal 
conductivities (one is twice that of the other at 1273 K) due to the 
increased heat transfer at these temperatures. The variation of 
thermal conductivity ^th concentration is more noticeable at 
small concentrations and the temperature rises considerably in 
the low concentration region (from 5 to 20%, by volume). 

Thermal conductivity of the almost crystallized sample 
(Fig. 27), containing 85 to 90% crystobalite as shown by micro- 
scopic investigations and 97% as shown by X-ray analysis, 
varies -with temperature in exactly the same way as in crystal- 
line quartz (See Fig. 18). In this material, thermal conductivity 
has the same values as that of quartz (see Section 5). The 
experimental results show that the relationship between thermal 
conductivity of crystalline and amorphous Si02 depends on tem- 


The thermal conductivity of quartz at low temperatures in 
the region of maximum phouon conductivity is four tinries the 
thermal conductivity of quartz glass (Berman's experiments 
[25]). The disorder caused by neutron emission brings about a 
gradual decrease in the mean free path of phonons and a corres- 
ponding decrease In thermal conductivity. On the other hand, 
the thermal conductivity of amorphous quartz in the region of 
A min (^- ^- about 273 K) is equal to that of crystalline quartz 
within experimental errors, and with increase in temperature, 
the latter considerably exceeds the former due to radiation. 

Stabilization of the structtire with the formation of a later 
order (crystallization of quartz glass) leads to a decrease in 
transparency and rapidly reduces the value of radiational thermal 

5 . Thermal Conductivity of Ref ra ctp ri es with High Silica ^ 

Refractory materials with high silica content (Dinas), form 
a widely used class of Industrial refractories. They serve as a 
lining material for coke oven batteries, blast furnaces, glass 
furnaces and other equipment. High silica content materials 
consist of 85 to 90% SI02. Refractories of this type are made 
up of various modifications of silica: quartz, crystoballte, trldy- 
mlte, vitreous material, quartz glass. 

Characteristics of the thermal conductivity — temperature 
relationship, for single-phase (quartz glass, crystoballte, 
quartz) and multiphase (Dinas, highly dense Dinas, Dinaso- 
chromite) refractories were lavestigated to ascertain the cause 
of the difference in thermal conductivity of different Dinas re- 

Some properties of the Investigated materials are given in 
Table 13 sind experimental results for the relationship of thermal 
conductivity with temperature are shown in Fig. 28 and in 
Table 14. 

It was found that thermal conductivity of crystalline inodi- 
fications of silica (crystoballte measurements were done on fully 
crystallized quartz glass, those on quartz were done on crushed 
quartzite) increases almost linearly with temperature. The small 


Some properties of refractory materials having high silica content 



al composition, 


Packing Apparent 
density porosity 
g/cm3 % 









Dinas (I) 








Dinasochromite (I) 










Highly dense Dinas 











Natural quartzite, 

crushed (111) 








Close to 

Natural quartzite. 

fused amorphous 

quartz (IV) 










Lightweight Dinas 

(from Krasnoar- 

meisk) (V) 










Lightweight Dinas 

(from Pervoural) 













98.24 0.30 
inal quartz glass 







♦Taken sam^e as in 

the orig 


Thermal conductivity of materials having high silica content, (alter reduction to sero 
porosity, by the formula "Xi,* "Xg(l-p) 


Thermal conductivity. kcal/m.h.K. at temperature K (°C) 

373 473 573 673 773 873 973 1073 1173 1273 1373 1473 1573 1673 
(100) (200) (300) (400) (500) (600) (700) (800) (900) (1000) (1100) (120C) 03001(1400) 


quartz glass 

Quartz (natural 

crushed quart- 


Quartz glass 


Highly dense dinas 

0.82 0.86 0,90 0.94 0.98 1.02 1.06 1.14 1.22 1.30 1.40 1.50 1.61 1.78 






















1.40 1.50 1.61 1.78 

1.92 2.05 2.17 2.35 
2.05 2.25 2.44 2.65 

Dinasochromite 1.11 1.14 1.20 1.25 1.29 1.35 1.45 1.52 1.61 1.74 1.86 1.98 2.10 2.27 

W13 i213 «75 1173 

(800) (1000) (mo) (mo) 
Temperature, K (°C) 

Fig. 28. Variation of thermal conductivity with temperature , in the case of 
high silica -content refractories. 

1 - Dinas; 2 ~ highly dense Dinas and Dinasochromite ; 3 - quartzite; 
4 - crystobalite; 5 .- quartz glass. 

difference hetween the behaviors of quartz and crystobalite in 
that the thermal conductivity of quartz has a minimum between 
773 to 873 K (5 00 to 600°C) which can be explained by the 
transition Pifc; a, for quartz at 846 K (5730C). A sixnilar aspect 
was also observed by other investigators [35] during thermal 
conductivity determinations of granite. Such changes, which 
oqcur around 573°C, are not detected in Dinas and Dinaso- 
chromite because of the small amount of quartz. The possible 
occurrence of this effect is further reduced on account of poro- 
sity and rennains within experimental errors. Crystobalite and 
quartz (excluding highly porous, lightweight Dinas) have the 
smallest value of thermal conductivity. Considering that quartz 
and crystobalite contain the least amount of impurities and have 
a porosity close to zero, it can be surmised that such tem- 
perature characteristics appertain to materials made from modi- 
fications of pure silica. The identical results obtained for 
thermal conductivity of quartz and crystobalite prove that 
differences in the crystalline structure of silica, e.g. the shifts 
in the tetrahedrals SiO^ and certain variations, displace Si — O 
into different modifications of silica, so that they do not affect 
the value of the mean free path of phonons. 

It is difficvdt to give a rigorous treatment to the studies on 
thermal conductivity of Dinas which includes eeveral modifica- 
tions of silica, vitreous phase and heat conducting oxides like 
chromium oxide hematite. Experinneatally, a higher val\ie of 
thermal conductivity is obtained than for pure inodificationa 


(Fig. 28). Among the various types of Dinas, the highest ther- 
mal conductivity is obtained for the highly dense and least porous 
Dinas containing hematite. Din&s and Dinasochromite have the 
same thermal conductivity although they have different porosity 
and chemical compositions. 

It appears that for a precise understanding of the laws 
governing thermal conductivity variations In this case, it is 
necessary to investigate thermal conductivity in the two-phase 




1. Features of Heat Transfer Through Ceramics 

A large majority of refractory insulators^ used in industry 
and science are substances having a large number of connected 
or isolated pores. 

The interest in the problems of heat transfer through 
poAvders and ceramics is due to their applications which range; 
on the one hand, from the highest temperatures (lining for induc- 
tion furnaces) to the lowest temperatures (thermal insulation of 
vessels for storing cryoganic liquids and, on the other hand, 
from chambers exhausted to 10"^ mm Hg Col to various kinds of 
equipment with highly conducting gases like helium and hydrogen 
at pressures greater than the atmospheric pressure. 

Such universal and, not seldom, intuitive applications of 
ceramics and powders, in the industry demand deeper studies 
on the characteristics of heat transfer through them. 

A ceramic body can be considered as consisting (Fig. 29) of 
grains, cracks or pores (closed or connected) and contacts bet- 
ween the grains (formed either during baking, or mechanically). 
For each element of a ceramic material, there is a characteris- 
tic form of heat transfer. Two mechanisms are possible in 
grains: conduction and radiation. Thermal conductivity of re- 
fractory insulators, the most comnnon of the refractories, has 
been discussed in the previous chapter. * 

■^ When considering the transfer of heat by a porous material, we use the 
term "effective thermal conductivity", meaning thereby the total effect of 
heat transfer, as distinguished from the term 'thermal conductivity ', 
usually used for compact bodies. 


Fig. 29. Elements of a ceramic. 

1 - grain of the body; 2 - contact of nan -baked grains; 3 ■• contact of 
baked grains wUh formation of the neck; 4 - closed pare: 5 - commu- 
nicating pore; 6 - crack in the grain. 

Grains, as a rule, form semicrystalline complexes, in 
which,according to Lee and Kingery [20], radiational heat 
exchcinge is negligibly small. Hence, heat transfer through 
grains is effected by conmaction. Taking into account the phonon 
conductivity mechanism in refractory insulators, it can be said 
that thermal conductivity~>«f grains decreases (except for zirco- 
nium dioxide, silica,etcj almost directly with rise in tem- 

Three forms of heat transfer can, in principle, exist in 
pores and microfractures: thermal conduction of gas in pores 
and microfractures, convection of gases in pores and micro- 
fractures, and radiation between walls of a pore. 

Instead of a contact between grains, a neck of the grain 
material (ceramic) as well as a mechanical contact (powder 
mass) could form betw^een the grains. In the first case, the 
thermal conductivity through the neck between two adjacent 
grains of a ceramic depends on its cross section and on the gas 
layer around the neck. As for the mechanical contact betw^een 
the grains, a contact has considerable thermal resistance, and 
so the thermal conductivity would be mainly realized through 
the gas. 

All the elements of a ceramic and all the important forms 
of heat transfer realized under definite conditions taJce part in 
the total heat transfer in a ceramic material or powder. They 
result in an "effective thermal conductivity". Predominance of 
one or the other constituent of the ceramic and of one or the 


other form of heat transfer depends upon the structure of the 
material, the temperature and the phyeical properties of the 

Some aspects of heat transfer through dispersed material 
have been systematically and fully discussed in the monograph 
[31] and in other publications. Since very little study has been 
done on refractory cerannics and powders from the point of view 
of thermal conductivity, and hardly any systematic study has 
been done at higher temperatures, it would be very interesting 
to evolve some laws of heat traxisfer through dispersed phase. 

2 . Influence of the Degree of Exhaustion within the Pores, 
on the Effective Thermal Conductivity of Refractory 

Thermal conductivity of refractory ceramics at pressures 
les-s than the atmospheric pressui'e has practical importaJice 
(for example, for using them in vacuum pouring of steel, for 
internal lining of vacuum type induction furnaces and in electri- 
cal resistance furnaces) and its study is necessary for cin under- 
standing of the heat transfer processes through ceramics. 

Data are available in literature about the effect of vacuum 
on the effective thermal conductivity of powders at low^ tem- 
peratures (Smolukhovskii effect) [32, 33] and about the varia- 
tions in thermal conductivity of some refractory oxides in 
vacuum [34]. But the effect of the extent of exhaustion on 
thermal conductivity of refractory ceramics, v/here grains 
form a continuous body, has not been investigated. 

Refractory materials covering a w^ide range of thermal 
conductivities (0.5 to 6 kcal/m. h. K) and porosities (approxi- 
mately 10 to 50%) were selected for investigation, as these 
ranges connpletely represent the class of ceramics called re- 
fractory oxides. Thermal conductivity variations with tem- 
perature were naeasured by the m.ethod described in Chapter I 
with the apparatus placed inside a vacuum chamber of large 
volume (0.5 m^). The chamber was so air-tight that it could 
maintain any pressure from 10"^ to 760 mm Hg Col during the 
experiments, without recourse to pumping. 


The temperature — thermal conductivity characteristic at 
atmospheric pressure -was deternnined in an open chamber. 
Thereafter, without changing the specimen, air was pumped out 
to the required pressurcjand the characteristic was recorded. 
Pressures less than 1 nrim Hg Col were measured with a mano- 
metric lamp Type L,T-2 and a matching vacuummeter Type UTV. 
Pressures greater than 1 nnmHgCol were measured with a 

After recording the temperature chai'acteristic at the mini- 
mum pressure (in our case, 10"'* mmHgCol), the pressure 
inside the chamber was gradually increased to the atmospheric 
pressure and the measurements wexe repeated at atmospheric 
pressure to check the results. The results obtained (Fig. 30) 
for thermal conductivity variation with degree of exhaustion 
showed that, in a certain range of exhaustion, there is a con- 
siderable variation and an appreciable change in the character of 
the temperature — thermal conductivity relationship. 


W 7 

■^ f.6 










— ■ 





^ a| 




1. 4 






»-/ o-J 0-5 
•-1 m-li 







1 1 



200 m BOO 800 mo mo 

Temperature, ^C 

Fig. 30. Effective thermal conductivity ofrefractcnry ceramics at various 
temperatures, under different degrees of exhaustion. 

a -for magnesite: 1 - at atmospheric pressure; 2~ at 40 mm HgCol; 
3 -at 4 X 10'^ mm HgCol; 4 - at 1 x 10 "^ mm HgCol. 

b -for DtKOS-j 1 -at atmospheric pressure; 2 - at 60 mm HgCol; 
3 -at 4 X 10 mm HgCol; 4-at 1 x 10-1 mm HgCol; 5 - at 
1 X 10-^ mrn HgCol. 

c - for far sterile; 1 - at attrsdspheric pressure; 2 - at 1 x 10 mm- 


A consideration of the main factors affecting heat transfer 
through ceramics leads to the conclusion, that the only cause of 
variation in effective thermal conductivity is the removal of air 
from the pores . However, according to the molecular-kinetic 
theory of gases [40], thermal conductivity should depend on 
pressure when the meain free path of molecules becomes of the 
same order or higher than the distance between the particles 
between which heat exchange takes place through the gas. 

In general, the free path length of gas molecules at differ- 
ent pressures and temperatures is: 

J ^"T 

C = , , r- (8) 

where, I, = mean free path 

k = Boltzmann constant 
p = gas pressure 
T = Absolute temperature 
S" = molecule diameter. 

Substituting the values of the constants, and considering the 
mean diameter of nitrogen and oxygen molecules (the main 
components of air) as the "diameter of air molecules", 

l==i-58 yio'^'J^- (9) 

The mean free path of air molecules at any given tem- 
perature and pressure could be calculated with this formula. 

Now^ consider the experimental results for thermal conduc- 
tivity at various degrees of exhaustion (Fig. 30), assuming that 
the distance d bet-ween heat exchanging surfaces is equal to the 
pore diameter. 

In an atmosphere of air at a pressure of one atmosphere, 
the thermal conductivity of Dinas (Fig. 30) at first falls by a 
negligible amount, but at temperatures more than T = 5 73 K 
(300°C), it increases with tennperature almost linearly. At a 
pressure of 60 mm Hg Col, the effective thermal conductivity of 
Dinas retains the value and nature of the temperature charac- 
teristic of the material at atmospheric pressure. Mea- 
surements at a pressure of 4 x 10" •^ mm Hg Col sho^wed appre- 

* i. e. , intercommunicating pares. 


ciable decrease in thermal conductivity. With further reduction 
in pressure (4 x 10" to 1 x 10"^ mm Hg Col) the thermal conduc- 
tivity decreases by a small amount. The pressure range in 
which effective thermal conductivity decreases rapidly (60 mm 
Hg Col to 1 X 10" mm Hg Col ), corresponds to the range of 
mean free paths: 0. 13 x 10-2 jq q 12 mm at 27°C; 0. 8 x 10'^ to 
0. 8 mm at 1500°C. According to the petrographic analysis, the 
range of mean free paths 0. 0013 to 0. 8 mm corresponds to the 
pore sizes in a Dinas specinnen (0. 01 to 0. 6 mm). Rigorous 
comparison is difficult owing to approximations in microscopical 
estimation of pore sizes, differences between the sizes of 
various pores, and other factors. 

A similar behavior was observed for magnesite. The 
reduction of pressure to 40 mm Hg Col did not lead to a decrease 
in thermal conductivity, but at 4 x 10" mm Hg Col considerable 
decrease in conductivity was noticed. Further reduction in 
pressure leads to very small variations in conductivity . 

Moreover on the basis of these preliminary experiments, 
it can be concluded that the conductivity of magnesite varies 
with pressure in the low pressure range 10 to 1.5 x 10" mm 
HgCol, which corresponds to a mean free path of 0. 01 to 3. mm 
at that temperature. Petrographic analysis data gave the pore 
sizes in the magnesite specimen between 0. 1 to 1.8 nnm. Re- 
lationship between ^ and log P is plotted in Fig. 31. 

The effect of a rapid decrease in thermal conductivity of 
the me diurrij filling the pores at atmospheric pressure, on the 
variation of effective conductivity of the material with tem- 
perature was also investigated, for a highly conducting ceramic 
as well as for a highly porous (lightweight) ceramic. For this 
purpose, the variation of effective thermal conductivity with 
temperature was investigated in air, at atmospheric pressure 
and at a pressure of 1 x 10" mm Hg Col, for several refrac- 
tories having different thermal conductivities and different A (T) 
characteristics. The results obtained are shown in Fig. 32. The 
connputed values of the relative change in conductivity of the 
studied materials are given in Table 15. 

The variation in effective thermal conductivity of a cera- 
mic, due to a decrease in the conductivity of the filling medium 
of the pores, brings about the following three effects, which are 


to' W^ 10 ' 10 

log P mm HgCol 

Fig. 31. Variation of thermal conductivity at 20CPC, under different pressures, 
for magnesite (1) and Dinas (2). 



5^ 2.0 
■^ 1.0 


cM to 


mo 300 SOO ' 700 900 two 1300 

Temperature, °C 

Fig. 32. Variation of thermal conductivity tvith temperature -- in air at 

atmospheric pressure (1), and at a pressure of 1 x 10-4 mm HgCol 
(2) --for materials with different thermal conductivities and having 
different ^(T) characteristics. (Properties shown- in Table 15). 



Relative variations in thermal conductivity ( > ) of alumina- 
silicate refractories, at a pressure of 1 x 10-4 i^rn HgCol 

Component Absolute Reduction of X in 

content, % Porosity value of ^ vacuum 

AI2O3 Si02 % in air, {lxlO~4 mmHgCol) 

kcal/m.h.K with respect to "X 
in air, % 

97 (e) 





83.19 (d) 





68.3 (c) 





42.9 (b) 





35.9 (a) 







*The value in the numerator is for 573 K (300°C); while that in 
the denominator is for 1073 K (800°C), 

well defined at temperatures at which the radiational heat trans- 
fer can be neglected: 

a) the greater the thermal conductivity of air inside the pores 
(corundum, Fig. 32; magnesite, Fig. 30) at atmospheric pressure, 
the greater is the decrease in thermal conductivity of material 
at a pressure of 10' mm Hg Col. 

b) for substances (corundum, Fig. 32; magnesite. Fig. 30) 

following the "X- — '— law at atmospheric pressure in air, this 

relationship changes in the opposite direction, i. e. , at maxi- 
mum exhaustion an increase in thermal conductivity is observed 
with an increase in temperature. 


For comparatively dense materials (apparent porosity 
24 to 25%) in which ordinarily ^«-^^ , the variation in the 
character of thermal conductivity-temperature relationship at 
a pressure of 1 x 10"* mmHgCol resembles the variation in 
highly porous materials compared to that of dense ones (Fig. 33) 
and it resembles the variation in powders compared to that of 
baked ceramics (Fig. 36). In materials with a positive tem- 
perature relationship (see Fig. 30) (high alumina and firebrick 
materials, Oinas), %he exhaustion of gas in the pores does not 
affect the temperature relationship (Fig. 34), 




> o — i-o 

♦ 75 





IS 73 
1 1 100) 

873 1073 1273 t'i73 
I ZOO) 1100} (600) (800) (WOO) 11200) 

Temperature, K (°C) 

Fig. 33. Variations of effective thermal conductivity with temperature, for 
high alumina content ceramic, in the case of: dense material with 
porosity 17% - fl): porous material with porosity 57% - (2). 

c) throughout the temperature range, the effective thermal 

conductivity of highly porous ceramics at 1 x 10"'* mm Hg Col 
decreases by 22 to 24% with respect to that at atmospheric 
pressure. This decrease is small in comparison with that in 
dense ceramics. 

The reason for variation in effective thermal conductivity 
is that, firstly, the thermal conductivity of the gas is reduced; 
and secondly, the contact thermal conductivity (the component 
characterizing heat transfer through the gas layer around the 
actual contact) varies considerably >vith decrease in thermal 
conductivity of the gas. Moreover, the decrease in thermal 
conductivity of air (which itself is quite lew), plays an indirect 
role in reducing the effective thermal conductivity. This happens 
according to the molecular -kinetic theory, w^hen the mean free 
path of the gas molecules in the ceramic becomes comparable to, 
or greater thaji, the distance between the walls of the pore 
through which the heat transfer takes place. 


1113 mj 

iSOO) (ItOO) 

Temperature, K (°C) 


Fig. 34.Variation of effective thermal conductivity with temperature, in the 
case of ceramics with a body conductivity directly proportional to the 

1 - Dinas; 2 - Lightweight Dinas. 

The temperature relationship for materials with high \, ^ 

but having Ar>^-s^ , changes with decrease in the thermal 
conductivity of air and so also at low temperatures when the 
component due to radiational heat transfer becomes small and 
the conductivity of air no more depends on the pressure. 

The steep decrease in thermal conductivity of highly 
conducting materials is due to the fact that the reduction in 
thermal conductance of the contacts impedes the appearance of 
the natural thermal properties of the cerannic (analogous to 
thermal conductivity of lightweight refractories and powder 
mass), because of the reduction in effective cross section for 
heat flow (Fig. 35). 

heat current 

Fig. 35. Diagram of heat flow through ceramics, at normal pressure in the 
pores — (a), and under a vacuum of about 1 x 10'^ mm HgCol — (b). 


In highly porous (lightweight) ceramics, appreciable de- 
crease in contact thermal conductivity does not take place and 
therefore, such a ceramic has a minimum reduction in the effec- 
tive thernnal conductivity (see Figs. 30, 32). At high temi- 
peratures (1073 to 1273°C), the temperature relationship curves, 
under standard conditions (760 mm Hg Col. ) and in vacuum, for 
corundum, Dinas, magnesite and some high alunnina- content 
materials are quite close (Figs. 30, 31). This obviously shows 
that, in the heat exchange at contacts, the conductivity involves a 
radiation component for heat transfer through the gas layer 
surrovmding the actual contact. The contact thermal conductivity, 
due to the thermal conductivity of gas in the pores, decreases 
with temperature rise for substances having ^<-»^ i. but it 

changes less noticeably in nnaterials having X'~' T (Table 16). 


Variation of contact thermal conductivity of refractory ceramics 

with temperature 



Value of contact thermal conductivity, 
kcal/m.h. K at mean temperature K (°C) 


473 673 873 1073 
(200) (400) (600) (800) 



C o rundum 


6.5 3.5 1.7 0.7 
3.54 2.07 1.58 1.22 
0.95 0.65 0.55 0.30 





It is clear from the observed data that the effect of reduc- 
tion of pressure in ceramic pores is due to the same molecular- 
kinetic effects as in powders (Smolukhovskilf effect [32]). Never- 
theless, qualitatively they are more varied, particularly regard- 
ing the character of the temperature relationship. These effects 
enable us to appreciably change the thermophysical properties of 
ceramics and thei^" temperature relationships over quite a wide 


The relationship of effective thermal conductivity with the 
degree of exhaustion could be utilized to improve the thermal 
properties of refractory ceramics. 

3. Effect of Actual. Particle, Contact on the Effective 
Thernnal Conductiyity of D ispersed Refractory 

Contact thermal conductivity, according to U. P. Shlykov 
and E. A. Ganin [36 to 38], is the sum of thermal conductivities 
due to actual contact and due to the gas layer around the contact. 

The effect of the degree of exhaustion and of the gas layer 
around the contact, on the effective thermal conductivity, vras 
dealt ^/rith in the preceding section. The difference between a 
powder mass and a pressed, baked ceramic of the sanne 
materials, having the same porosity, is only that in the first 
case the grains contact each other without baking and in 
the second case the grains are baked, forming a neck contact 
in the grain material. By measuring thermal conductivity of 
powders and specimens baked from them, the effect of the bak- 
ing of graihs on thermal conductivity could be determined, i. e. , 
the role of factual contact on the heat transfer through ceramics 
can be determined. 

The apparatus described above was used over a wide range 
of temperatures, for measuring the thermal conductivity up to 
1773 K (1500°C) for ceramics and a modified version was used 
for powders. In both the cases, the test cylinders had approxi- 
mately the same size. For ceramics, the cylinder had a height 
200 mm, outside diameter 75 to 80 mm; whereas the powder was 
filled in a hollow cylinder of height 203 mm, outside diameter 
91 mm. 

The materials investigated were: magnesite with 2% Zrt, 
magnesite on spinel bond; periclase-forsterite and periclase- 
spinel two-phase combination. The results of investigation are 
shown in Fig. 36, 

For the ceramic specimen made from powder with grain 
size 1 to 0. 2 mm, the temperature relationship retains the 
character of the parent material (Fig. 36) in spite of the quite 
high porosity (45 to 60%). At lower temperatures, the^r~»-*- 








im 1313 
(300) am) 

Temperature, K (°C) 
Fig. 36. Thermal conductivity of per icbzse -spinel, two phase system. 

1 - powder with grain size 1 to 0.2 mm. packing density 1.2 g cm' ; 

2 - ceramic made from powder of grain size 1 to 0.2 mm, packing 
density 1.9 g cm "■'. 

relationship is observed more or less clearly; at higher tem- 
peratures the effect of radiation through pores changes the X— 
temperature relationship appreciably. A powder with grains, 
equal to the grains of the ceranmic, had sui effective thermal con- 
ductivity lower than that of the ceramic but the teniperature re- 
lationship had the opposite sign. Maximum decrease in thermal 
conductivity is observed at the lowest temperatures. With in- 
crease in temperature, the difference in the effective thermal 
conductivity of a powder and its ceramic decreases. 

In general, the grain contact area for powders is snnall 
due to the irregularity in grain shape, and has a quite high hard- 
ness value and low ductility. In other words, thermal resistance 
at the point of grain contact is so large due to the negligibly 
small contact area that the grains are disconnected as far as 
heat transfer is concerned. Therefore, other features of the 
ceramic, i. e. , the conductivity of the gas in the pores and 
around the contact are mainly important in this case. Con- 
ductivity of the gas in the spaces around the powder grains 
affects to a much less extent and so the effective thermal con- 
ductivity in this case is small. 

In the ceramic specimen, where the grains form a conti- 
nuous body, a neck is formed in the contacts due to baking, 
which has a grain size comparable to that of the grain itself. 
In this case the conductivity of the body increases due to heat 
exchange through the gas layer around the actual contact and 
forms the major part of the effective thermal conductivity. 

Experinn^ents show that the temperature relationship of 
thermal conductivity of Ceramics from magnesite and periclase- 


spinelide with a porosity up to 60% has the same character as 
that of the dense samplesof the same materials with zero poro- 
sity [3]. At temperatures above 673 K, the proportion of contact 
thermal conductivity is somewhat reduced due to an increase in 
radiational conductivity. Nevertheless, these aspects cannot be 
treated separately, because the radiation in the contact zone 
considerably increases the contact thermal conductivity. 

Even at the highest temperature considered in these 
investigations, the effective thermal conductivity of powder is 
just 0. 53 to 0. 63 that of the ceramic, only because of the 
difference in thermal conductivity of the actual contact. For 
zirconium dioxide powder and the ceramic made out of it, the 
corresponding ratio of the effective thermal conductivities is 
different from the one described above (Fig. 3 7). In this case, 
there is practically no difference between the effective thermal 
conductivity of powder and ceramic, throughout the temperature 

Sj J7J 513 113 913 1113 1313 1513 1113 

o; (100) (300) (SCO) (100) (300) -(1100} (1300) 11500) 

^ Temperature, K (°C) j 

Fig. 37. Thermal condacUviiy of zirconium dioxide stabilized with calcium 

1 - powder with grain size ^0.2 mm, density of loose material 
2. 93 g cm~^; 2 - ceramic from powder with grain size ^0.2 mm, 
packing density 2. 96 g cm '^; 3 - powder with grain size 1 to 0.2 mm, 
density of loose material 2. 30 g cm '•',■ 4 - ceramic from pou/der with 
grain size 1 to 0.2 mm, packing density 2. .'i3 g. cm -3. 

Two aspects have to be taken into account while consider- 
ing the effect of contact thermal conductivity on the effective 
thermal conductivity: a) the 4i£ferenc«, of absot one to one-and- 
a-half orders, in the absolute values of thernnal conductivity 
for periclase- spinel, periclase-forsterite, magne site and spinel- 
bonded magnesite on the one hand and zirconium dioxide on the 
other; b) the difference in the character of temperature relation- 


The body thermal conductivity of rirconium dioxide is so 
small (1.5 kcal/m. h.K) that it differs by less than one order 
from that of the powder (0. 25 kcal/m. h. K) and from the contact 
thermal conductivity. For the rest of the materials, effective 
thermal conductivity of the powder (0.25 kcal/m. h. K) is less 
than that of the body by at least 2 orders. 

The law of variation for phonon conductivity above the 
Debye temperature, when A.< — ^""^ holds good, applies for a 

majority of refractory oxides (except rirconium dioxide, glass, 
silica and a few others). Consequently, the variations in effec- 
tive thermal conductivity for periclase- spinel, periclase- 
forsterite and magnesites, with reduction in grain contact cross 
sections and simultaneous change in temperature characteris- 
tics have a general nature, 

A qualitative similarity can be observed between the 
variation of effective thermal conductivity with decrease in 
conductivity of actual contact and thermal conductivity of gas 
layer around the contact, by a comparison of results of this 
section with those of Section 2. Fig. 38 shows the variation of 











1073 1273 m3 1673 
(sag) (WOO) (l!00) (liOO) 

Temperature, K (°C) 

Fig. 38. Variations of thermal conductivity with temperature, for different 
types of magnesite ceramics. 

1 - ceramic of porosity 24%, at atmospheric pressure; 2 - the same 
under a pressure of 1 x 10-^ mm HgCol; 3 - highly porous (light - 
weight) ceramic of porosity 60%; 4 -powder with compactness 60%. 

thermal conductivity with tennperature, for magnesite ceramics 
with different contact thermal conductivities determined by the 


experimental conditions. The following ways of increasing 
(or regulating) thermal ins vilation properties of refractory 
ceramics are available: a) increasing the porosity; b) decreas- 
ing the thermal conductivity of gas in the pores by establishing 
a known vacuum in the pores; c) decreasing the area of actual 
contact by substituting .powder for ceramiic; d) decreasing the 
conductivity of gas in empty spaces between the powder grains. 
This question is not being dealt with by us, though investigations 
[41] indicate that the effective conductivity of quartz powder is 
reduced in vacuum. 

4 , Influence of Highly Conducting Gas on the Effec t iy e 
Thermal Conductivity of Refract ory Ce ramics 

Experiments in which thermal conductivity of gas in the 
pores w^as reduced by at least three orders •were discussed in 
the previous section. Such a reduction completely changes the 
picture of heat transfer through ceramics. Actually, at a pore 
size not more than 1 mm, only the thermal conductivity of the 
"body" takes part in heat transfer, while the contact conducti- 
vity through the layer of gas around the contacts and the radia- 
tion across it does not play any role at all. 

Experimental results, under conditions in which conducti- 
vity of the gas in the pores Avas increased to seven times that of 
air, are discussed in this section. The measurements were 
conducted in the following order: the apparatus, ready for in- 
vestigations-,^ was placed in the vacuum chamber and the electri- 
cal leads and the measuring circuit were connected at the 
vacuum inlets. The A (T) relationship was studied at atmos- 
pheric pressure and then at a pressure of 1 x 10"^ mm Hg Col. 
Thereafter, \ (T) was measured on the same setup, in a 
hydrogen atmosphere at a pressure of 1 atm. For this, the 
vacuum chamber, evacuated to 1 x 10""* mm HgCol^was filled 
with hydrogen. As the temperature increased, the excess hydro- 
gen was let out through a water seal (in order to keep the pres- 
sure inside the channber constant). Results of the investigations 
are given in Fig. 39- It also shows for comparison, the tem- 
perature relationship curves at a pressure of 1 x 10"^ mm— 
Hg Col. When the pores are filled with hydrogen, the thermal 
conductivity increases; the ^^ (T) curves with hydrogen and 
with air in the pores, both at atmospheric pressure, are paral- 
lel, barring a few exceptions (Fig, 39 c, d). At a mean tem- 




?fl(» WO «(W 800 1000 l!00 




25/7 ♦/» ff/;/; 800 mo noo 
t °^ 



2fl0 Wfl fi(W 800 1000 1700 



200 m 600 800 1000 mo 
t °c 



/"//ff WO BOO BOO 1000 1200 
* " 'C 

i*/?/? W/? 600 BOO WOO 1200 
tav °C 

Fi^gf. 39. Effective thermal conductivity of refractory ceramic in air, hydrogen 
and vacuum. 

a b c d e f 

apparent porosity, % 24 12.7-13.5 10-15 10-12 15.5 57.6 
AI2O3 content, % 97 82.2 63 45 37 82 

i - in a« atmosphere of air at atmospheric pressure; 2 - in an atmos- 
phere of air at a pressure of 1 x 10'^ mm HgCol; 3 - in an atmos- 
phere of hydrogen at atmospheric pressure. 

perature of 1073 K (SOC^C), the thermal conductivity increases 
by 17 to 35% for a porosity of 10 to 20%, and by 60% for a poro- 
sity of 60%. T^is change, when the pores are filled by hydro- 
gen, is explained by the higher thermal conductivity (about 7 
times) of the hydrogen. 

Using the additive fornnula, which holds good when the gas 
phase fills isolated spherical pores. 

A = qA, + c^X 


(Cj, C2 being the concentrations of the phases; \a , A*, their 
thermal conductivities) and calculating "X when hydrogen fills 
the ceramic pores, the following results were obtained: The 


less the thermal conductivity of the specimen (within a range of 
10% of the thermal conductivity of the "body"), the closer is the 
calculated value to the experimental value (the experimental 
values are in fact somewhat higher than those estimated). For 
a mean temperature (1073 K,i. e.,800°C), the excess of experi- 
mental values over the estimated ones is as follows: 

kcal/m.h. K 3.14 2.00 1.94 1.10 1.00 

(excess) % 25 32 16 14 10 

A similar divergence was observed by Wygant and Crowley 
[42] while determining thermal conductivity of concrete insula- 
tion, at temperatures up to 673 K (400°C), in hydrogen and 
helium atmospheres. Theoretical formulae of Russell [43] and 
Loeb [44], agree well with these experimental results only in 
the case of materials of low thermal conductivity and open porea 
For materials with closed pores (on \^ich our experiments were 
done), except in the case of high alumina- content lightweight 
refractory, the formulae are gcod enough only at pressures 
above the atmospheric pressure. 

The divergence between experimental and theoretical 
values could be due to the fact, that the share of contact con- 
ductivity through the ga? phase around the contacts is not 
accounted for anywhere. When pores are filled with hydrogen, 
the contact thermal conductivity is more than when they are 
filled \^th air. (This is also the case, when the pores contain 
air rather than vacuum. ). Contact thermal conductivity is 
determined by the thermal conductivity of the gas in the pores 
as well as by the thermal conductivity of the "body". 

Thus, the theoretical formulae of Loeb [44], Russell [43] 
as well as the additive formula used by us do not fully take into 
account the real structure of the ceramic and the complete heat 
exchange process through it. 

Experimental restilts obtained, on changing the effective 
thermal conductivity by filling the cerannic pores with more 
conducting gas, show that the increase in ^ is not much for 
dense materials, but it is quite large for porous ones. 

As such, the use of highly conducting gases (helium, 
hydrogen) in conjunction with insulation ceramic adversely 


affects the performance of the ceramic. In such cases, dense 
materials with low thermal conductivity are more effective. 
The character of ^ (T) in certain cases is somewhat changed 
(Fig. 39 c, d) at lower temperatures, due to better heat exchange 
through the gas layer aroiind the contact. 

5. Effective Thermal Conductivity o f Refractory Powders 

Refractory powder insulation is widely used in considera- 
tion of its special characteristics: i) the possibility of insulating 
the spaces of complicated shapes and ii) a nninimum of effective 
thermal conductance (as compared to a ceramic having the 
lowest thermal conductivity). However, for correct choice of the 
insulating powder and its size, a knowledge of the factors affect- 
ing the effective thermal conductivity is essential. Refractory 
powders of zirconium dioxide, magnesite with zirconium dioxide 
additive, magnesite on spinel bond, periclase-forsterite, 
periclase-spinel, having grain size of 2 to 5 mm, 1 to 0. 2 mm 
and less than 0.2 mm, were studied. The variation Avith tem- 
perature, of the effective thermal conductivity of the powders 
of all grains sizes was studied at the hot face temperatures of 
473 to 1473 K (200 to 1200°C). The results are shown in Fig. 40 
and could be summed up as follows: (1) Variations in effective 
thermal conductivity of po^wders do not depend on the type of 
material (at least up to 12 73 K (1000°C) but depend only on the 
grain size, (ii) At 3 73 to 473 K (100 to 200°C). the effective 
thermal conductivity does not depend even on the grain size and 
is equal to 0. 2 kcal/m. h. K (0.23 Watt/m. K) or, it may be that 
the difference in conductivity of different powders is less than 
the sensitivity of the method used, (iii) The small value of 
effective thermal conductivity at low temperatures could be 
explained by the action of two processes, which have little 
effect from the heat exchange point of view, viz, the heat 
transfer through the grain contacts and the thermal conductivity 
of air in the empty spaces. How^ever, both these processes are 
interrelated cund the total effect beconnes as much as 0. 2 kcal/ 
m. h. K, even though the thermal conductivity of air at these 
temperatures is smaller by one order (Fig, 39). Thus the air 
in the empty spaces between grains affects the value of effective 
thermal conductivity. The experiments [32] and the measure- 
ments [41] showed that with decrease in gas pressure in the 
empty spaces, the effective thermal conductivity of powders 
could decrease to one-tenth the normal value. 







1*73 573 873 1013 1273 /*73 
[200) {100) (BOO) (800) (WOO) (JP.OO) 

Temperature, K (°C) 
Fig. 40.Effective thermal conductivity curves for refractory powders. 

a -grain size <^0.2 mm; b -grain size, 1 to 0.2 mm: c - grain 

size, 2 to 5 mm. 

1 - periclase -spinel combination: 2 - perclase - forsterite cnnibina- 

tion; 3 - magnesite on spinel bond; 4 - magnesite with 2% zirconium 


Since the above experiments show that the effective ther- 
nnal conductivity of powder does not depend on grain size, it 
appears that the contact thermal conductivity plays a minor role. 
Consolidation of powder having grain size smaller than 0. 2 mm, 
leads to an increase in powder density by 20% and that of 10% 
in thernnal conductivity. This confirms that the possible effect 
of contact thermal conductivity on effective thermal conductivity 
is negligible compared to the effect of gas in the empty spaces. 
This is also shown by experiments on the effect of porosity of 
the grains themselves. Effective thermal conductivity of dense 
powders and those of 60% porosity was measured to check up 
this point. It was found that there is practically no difference 
in effective thermal conductivity of the lightweight and the dense 
powders having grain size less them 0.2 mm -- apparently 
because, the structure of the powdered mass remains approxi- 
mately the same up to this grain size. With an increase in the 
grain size and also with increase in temperature, the difference 
between effective thermal conductivity of porous and dense 
powders reached up to 10%. 


At temperatures ^ 573 K (300°C), grain size affects the 
thermal conductivity. The temperature relationship of conducti- 
vity, i. e. ^ ( "7* ),al80 depends on grain size. For powders 
of grain size ^ 0.2 mm, the effective thermal conductivity 
increases linearly with temperature. It is peculiar that the 
straight line, representing thermal conductivity, is parallel to 
the temperature relationship for air throughout the temperature 
range, and is above it by one order. It can be concluded from 
this comparison that, radiational conductivity is absent in a 
powder mass having grain size less than 0.2 mm and porosity 
y^—^ 10%, while the spaces between the grains can be assumed 
to have th« same dimensions as the grain. This conclusion is of 
practical importance, and is also valid for ceramics. For 
powders, with grain size 1 to 0. 2 mm, the curve has a steep 
gradient, and it is more so for 2 to 5 mm. In these cases, the 
effect of radiational conductivity on effective conductivity is 
considerable. The radiational conductivity, at 373 to 1473 K 
(100 to 1200°C), of powders having grain size 2 to 5 mm is close 
to and in some cases even greater than the thermal conductivity 
of many refractory ceramics. The use of powders having this 
grain size is therefore not desirable. At the same time, 
operational characteristics of powders having small grain size 
are bad on account of increased susceptibility to thermal dis- 
integration, formation of settling cracks and consolidation. On 
the other hand, operational characteristics are quite promising 
for powders having grain size 2 to 5 mm. Hence the possibility 
of reducing inter-grain spaces by using a mixture of powders of 
different sizes was verified. It was assumed that the smaller 
grains (1 to 2 mm) fill the space between the bigger grains 
(2 to 5 mm), and thereby reduce the total volume and hence the 
radiational thermal conductivity. A mixture consisting of 55% 
of 2 to 5 mm powder and 50% 1 to 0.2 mm was taken. Effective 
thermal conductivity of such a mixture was close to that of the 
smaller grains, i. e. , the dimensions of the spaces can considei^ 
ably improve the thermal insulation properties of the powder and 
ceramic by creating a structure which would nullify the action of 
the effective heat transfer processes: radiation, phonon conduc- 
tivity, conductivity of the grains and the body, 

6. ^^i^?'^^^ 9^ Porosity. Shajae and Dimen sions of Pores 
^n^Effectiye Thermal Condu ctivity of Ceramics 

The existing formulae connecting thermal conductivity and 
porosity of refractories, (except the modified formula [45] ) do 


not take into account the radiation through pores and spaces. 
Till now, contact thernial conductivity has not been included in 
such calculations. General theoretical consideration of this 
aspect is also important due to the fact that the relationship 
"XtT) has been little studied experimentally, particularly in a 
wide temperature range. Some results of experimental investi- 
gations on the effect of porosity on effective thernaal conductivity 
of refractory ceramics are given in this section. 

The variations of thermal conductivity with temperature 
for two corundum ceramic structures are shown in Fig. 41. 

In respect of porosity (80 to 82. 5%) and content of AI2O3 
(95.5 to 96%) and SiOg (3. 10 to 3.40%), these two ceramics are 
almost identical. The shape of pores in hoih. the ceramics is 
round, eind the pores are closed. On an average, the pores of 
the one are twice the size of those in the other. In the ceramic 
with bigger pores, the pore size is more than the minimum 
size (around 1 mm) at which radiational conductivity is just 
detectable. For this ceramic, the number of contacts between 
grains, in a plane perpendicular to the heat flow, w^ould be as 
meiny times less as the difference in the mean pore diameters, 
i. e. two times. 

This led to a steep fall in conductivity at low temperatures 
(up to 700°C), as a result of the increase in pore sizes, reduc- 
tion of curvature in the baked contact zone and, consequently, 
of the sharp decrease in contact thermal conductivity through 
the gas layer around the actual contact (see Fig. 34). Because 
of this, the effective thermal conductivity at lower temperatures 
is more for the ceramic with smaller pores. For the low- 
porosity ceramic with high contact thermal conductivity, the 
relationship X(T) has the same character as that of the ceramic 
body material. 

At temperatures above 700°C, the curves of the effective 
thermal conductivity values of the two ceramics change con- 
siderably. It appears that radiational conductivity is absent in 
the ceramic with pore sizes 0. 3 to 0. 9 nnm (curve 1) amd that 
'X decreases right up to 1673 K (1400°C). On the other hand, 
radiational conductivity in the ceramic with pores 0. 6 to 1.4 mm 
becomes so high, that the character of the temperature relation- 
ship is changed. At 1473 K (1200°C), the thermal conductivity 
of the ceramic with large pores does not appreciably differ from 


that of the ceramic with smaller pores, although the former was 
found to be twice as much as the latter at 373 K (100^ ). 

The effect of the shape of pores on the thermal conductivity 
of high alumina- content materials was also studied. A sharply- 
defined region of porosity of about 10% was selected. The 
materials did not practically differ from one another in porosity 
and chemical composition, but the shape of pores was different. 
Judging from water permeability, i. e. , from the rate of rise of 
water in a block of the test material, the pores appeared to be 
closed and narrow in one case (Fig. 41 a, curve 1), since the 
resistance to the seepage of water was large (1. 72 mm/min) and 
the sample was found to be dense on microscopic examination. 


373 573 773 973 1173 1373 J573 
1 100) (3g0) (500) (700) (900) (1100) (1300) 

Temperature, K (°C) 

Fig. 41. Variation of thermal conductivity with temperature, in the case of 
refractory ceramics with different porous structures. 

a - High alumina -content, dense ceramic: 

1 -porosity, 10%; 82.8% AI2O3; water permeability, 1.72 mm/min. 

2 - porosity 9. 4%; 83. 2% AI2O3; water permeability, 9. 2 mm/min. 

b - Highly porous corundum ceramic: 

1 - porosity, 80%; 95. 5% AI2O3 + 3. 10% Si02; dominant size of pores, 
0. 3 to 0.9 mm; 2 - porosity, 82. 5%; 96% AI2O3 + 3. 40% SiOz: pore 
size'0.6 to 1.4 mm,. 


In the other case (Fig. 41 a, curve 2), water permeability- 
was large (9.2 mm/min). the ceramic was porous and the resis- 
tance to heat flow through the pores was more. Due to this 
difference in porosity, the denser ceramic had a larger thermal 
conductivity at low temperatures than the porous one. As a 
result of radiational conductivity, the increase in conductivity 
with rise in temperature is proportional to T^ in the case of the 
porous structure, and so long as the dense structure conformed 
to the relationship X.' — '-^ , the difference in thermal conducti- 
vities of the two materials almost vanished; but opposite charac- 
teristics were observed in the case when *X ^^ (T)*. 

The following conclusions could be drawn from the above 
results which show appreciable change of thermal conductivity 
with the shape and size of the pores: 

(1) at low temperatures (up to 600 to 700 C), other conditions 
rennaining the same, the ceramic with smaller pores has a 
greater thermal conductivity, 

(2) at higher temperatures (above 600 to 700°C) the ceramic 
with larger pores (above 1 mm) has a greater thermal conducti- 

This demarcation is due to the dominant action of different 
modes of heat transfer in the same temperature range in two 
cases. This means that vtnder low^ temperature conditions of 
operation, the insulation w^ith large pores is more effective and 
at high temperatures, the insulation with pores smaller than 
1.0 nam**, (which eliminate radiational conductivity through the 
pores) is vuidoubtedly better. 

Different thermo-physical properties and characters of 
the temperature relationship of ceramics at low (100 to 700°C) 
and high (700 to 1400°C) temperatures necessitate the use of two 
types of ceramics (high-temperature and low-temperature) de- 
pending on the temperature of operation. Such differential 

* The distribution of pores according to sizes also affects the effective ther- 
mal conductivity, but determination of the character of distribution is 
quite difficult and was not undertaken in the present investigation. 

**Precise value of pore size, above which the radiational conductivity domi- 
nates at high temperatures, is difficult to establish due to heterogenous 
structure of ceramics. 


application of ceramics would considerably improve the effec- 
tiveness of refractory insulation. 

Two types of refractory ceramics were selected for ex- 
perimental investigation of the relationship 'X(p), (where p 
refers to percentage porosity). They had different values of 
thermal conductivity and different ^(T) relationship. The two 
ceramics were: a) high alumina- content alumina- silicates with 
an approximate relationship ^•*<w'-^ and a thermal conductivity of 

the body material 2. 6 kcal/m. h. K; b) firebricks of alumina- 
silicates, for which A -^ T and thermal conductivity is around 
0. 9 kcal/m. h.K. 

The \{p) relationship at 4 73 K (2 00°C) for high alumina - 
content materials and firebricks is shown in Fig. 42, a and b, 
respectively. The temperature chosen was low, in order to 
exclude to a minimum the possible radiational heat transfer 
effects, which distort the character of the relationship. 

10 ?0 JO W 5060 1060 so 

Porosity (P), % 

/< 0. 

10 20 JO. 50 eo 10 80 90 

Porosity (P), % 

Fig. 42Jielationship of thermal conductivity with porosity at 473 K (20(f'C). 
a -for materials with high alumina -content; b - for firebrick. 

The value of thermal conductivity decreases linearly with 
increase in temperature for low- conducting firebricks. This 
means that throughout the porosity range 

A (p) = \ (1 - p) 

where, 'X = thermal conductivity of the ceramic body; 


p = porosity. 

For high a Ivunina- content materials, the character of the 
'X (p) relationship is nonlinear. 



A large rnajority of refractory materials consist of refrac- 
tory oxides, which are heat insulators (refractory dielectrics). 
The variations of thermal conductivity in these materials follow 
the laws of thermal conductivity of non-conducting crystals and 
their system. 

Experimental investigations on the thermal conductivity of 
refractory insulators show that two groups of substances can be 
distinguished, according to the nature of variation of thermal 
conductivity, at temperatures above room temperatures (and 
particularly, above the Debye temperature). 

One group of substances (MgO, AI2O3) has a relationship 
close to X<-«..^ , up to 1273 to 1473 K (1000 to 1200°C), at 
which the mean free path of phonons becomes equal to the inter- 
atomic spaces. Then X is constant right up to the melting point. 
The other group (quartz; zirconium dioxide; zirconates of barium, 
calciumjand strontium) is characterized by ^ -^ T, in the range 
3 73 K (100°C) to the melting point. A substance of this type is 
also characterized by a low value of ^ max ^^ ^°^ tem- 
peratures (10 K), and a ^ . (around 300 K), as well as by low 
Debye temperature (around 250OC). 

Substances of the type AI2O2 and MgO, on the other hand, 
have a relatively high ^ rnaix (^ times more thcin that of quartz), 
a higher temperature for '^rnax ^^^ ^ ^°' ■Al2*-*3' HO K for 
BeO); a "^ min (1300 to 1500 K) and Debye temperatures of 800 K 
for MgO and 750 K for AI2O3, which are far higher thein that of 

It is possible to get refractory insulators having a thermal 
conductivity different from that of pure substances, by forming 
multi- component, multi-phase systems or solid solutions. 


In very simple cases, it is important to distinguish between 
a solid solution and a two-phase system: a) formed by two insula- 
tors of the first group, for each of which 'X'^^ ; b) formed by 

two insulators of the second group, for each of which "X.-.^ T; 
c) formed by two components, one of which has "X ^>^ A- and the 
second has 'X'^^T. ' 

It has been shown, by investigating the binary system 
AI2O3 - Si02, that for a mixtureof components differing greatly ■ 
in thermal conductivity, of which one has a thermal conductivity 
corresponding to a mean free path equal to the interatomic dis- 
tance at lower temperatures (100 to 200°C) and in which 
"X '■^ T, the curve of thermal conductivity vs. concentration has 
a markedly luisymmetric character and does not have the charac- 
teristic minimum of solid solutions. 

It has been shoAvn by the example of thermal conductivity 
for two-phase system crystalline silica -- quartz glass, at 373 
to 673 K (100 to 400°C), that for two components of equal conduc- 
tivity, and a mean free path of the same order as the interatomic 
disteuice, the thernnal conductivity does not vary throughout the 
concentration range. 

In the higher tennperature range for the quartz -- quartz* 
glass system, in which one of the components has a thermal 
conductivity several times larger than that of the other, and in 
which for one of the components "X "^ T while that for the other 
^ ^>^ T'^ (n ^ 3), the thermal conductivity varies nonmonotoni- 
cally from li^glass *° ^quartz ^^^^ changes in concentration. 

It has been shown experinnentally, that the minimum ther- 
mal conductivity values of refractory insulators, observed at 
temperatures close to room temperaturei are roughly equal to 
1 kcal/m. h. K for substances having X'-^T; whereas above 
100 C, for substances having 'X'-v^4^> the thermial conductivity 
is equal to 5 kcal/m. h. K. Thus, from the point of view of ther- 
mal insulation properties, refractory insulators and their com- 
pounds have relatively high thermal conductivity. Moreover, a 
reduction in thermal conductivity and the control of thermal 
properties is possible by using the required structure for cera- 
mic and powder mass. 

A wide variation in effective thermal conductivity is possi- 
ble in refractory cerannics by utilizing different factors, which 


affect thermal conductivity. As shown in this brochure, these 
methods are: a) evacuation of ceramic pores; b) filling the pores 
with gases of different thermal conductivity; c) creation of a 
porous structure with pore size either smaller or greater than 
the limit at which radiational heat exchange is possible; d) regu- 
lation of contact thermal conductivity through the actual contact 
as well as through the gas layer around the contact. 

The indicated possibilities are realized to a greater or 
smaller extent, depending on the type of the refractory insulator. 
In the case, when a ceramic body represents an insulator of the 
first group (for which the thermal conductivity in the temperature 
range 0°C to melting point is inversely proportional to tem- 
perature), the methods of improving thermal insulation proper- 
ties of refractory ceramics at lower temperatures (up to 700 to 
800°C) are quite effective. For ceramics made from insulators, 
for which ^ '^-z T, the effect of these methods is somewhat 
lower in a wide range of temperatures. 

It has been shown, that while estimating the effective 
thermal conductivity of refractory ceramics, it is essential to 
know not only the composition and porosity, but also the domi- 
nant pore size, i.e. , the microscopic structure of porosity. 
This is necessitated by the fact that the action of the porous 
structure is not unique. If pores o£ large size (specially if the 
size is more than 1 mm) predominate in the ceramic, then at 
low temperatures the thermal conductivity of such a struc- 
ture is quite low and a variation in the character of the tem- 
perature relationship is possible. Under these conditions, at 
the low^er temperatures, a ceramic with large pores has an 
advantage over that with small pores. But, at temperatures 
above 873 to 1073 K (600 to 800°C), the thermal conductivity of 
coarse-grained ceramic increases due to radiation and the 
thermal insulation properties of the ceramic, having large pores, 

If such pore sizes predominate in the ceramic, wrhich avoid 
radiational heat exchange, then 7v (T) relationships for the 
ceramic and the body material are similar. 

Investigation on thermal conductivity of different crystal- 
line modifications of silica showed^that differences in the crystal- 
line structure of the type of shifts in tetrahedrals Si04,and cer- 
tain variations of distances Si— do not have any appreciable 
effect on the phonon dispersion. 



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